Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar
A: We can check whether the three vectors are co planar or not as below
Q: Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R =…
A: We find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q =(4,-2,1)…
Q: Find a nonzero vector orthogonal to the plane through points P(2,1,5), Q(-1,2,3), and R(0,3,3), and…
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Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)
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Q: A vector orthogonal to the plane through the points (-1,0, 0), (0, 0,-2), (2, 3, 4) is
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Q: A normal vector for the plane through the points (2, 5, 1), (3,7,0), and (2, 5, 2) is: O (-2, –1,0)…
A: Let the given points in the plane be A(2, 5, 1), B(3, 7, 0), C(2, 5, 2)
Q: Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a rectangular…
A: Question- Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a…
Q: A vector orthogonal to the plane through the points (-1,0,0), (0, -2, -2), (2, 3, 4) is < 2, – 10, 6…
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Q: Show that the vectors ⟨1, 2, 3⟩, ⟨1, 1, 0⟩, and ⟨3, 4, 3⟩ lie in the same plane
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Q: ind a unit vector with positive first coordinate that is orthogonal to the plane through the points
A: Given that the plane passes through the points, P(4,1,-1) Q(5,2,0) R(5,2,5)
Q: 13. Find an equation of the plane through the point (1,2,3) and perpendicular to the vector…
A: Given a point P( x, y, z) and a vector (a, b, c) which is perpendicular to the given plane
Q: Find a vector V that is perpendicular to the plane through the points A=(0,3,4) , B=(3,-5,−5) , and…
A: Find the vector AB and vector BC. The cross product of AB→ and BC→ gives a vector which is…
Q: Find a vector that is orthogonal to the plane containing the points. (Orthogonal means…
A: Given points are, P=3,0,1Q=4,-2,1R=5,3,-1 The orthogonal vector n^ will be calculated from the given…
Q: Find a vector v that is perpendicular to the plane through the points А %3 (0, 4, —3), В 3 (5, —5,…
A: Coordinator of the plane is given Find out the vector that is perpendicular to the plane
Q: 2. Consider the vectors [2, 1, 0, 0], [3, 1,0, 0], [0,0, 0, 1) in R". Find a vector v so that v, (2,…
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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, –2), (2, 3, 4) is
A: Query- Find a vector orthogonal to the plane through the points -1,0,0,0,-2,-2,2,3,4. Answer- Let…
Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…
A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]
Q: Find a vector equation for the line through the point Pla,-1,0,3) that is orthogonl t the hyperplane…
A: Suppose a line passing through the fixed point with position vector a and parallel to vector b, then…
Q: Consider the vectors (2, 1,0, 0), [3, 1,0, 0], [0,0, 0, 1] in R". Find a vector v so that v,…
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Q: Find a nonzero vector orthogonal to the plane through the points P, Q and R if P(1,0,0), Q(7,8,0)…
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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P=(2,0,-4),…
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Q: Find a vector v that is perpendicular to the plane through the points A = (4, – 5, –2), B = (2,3,…
A: We are asked to find the vector that perpendicular to the plane through the points
Q: Find a vector v that is perpendicular to the plane containing 3 -() 6 and 0 2
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Q: Find the orthogonal projection of the vector (2,4) about the line L parallel to the vector (-1,2)
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Q: Find the vector component of the vector U orthogonal to a: и %3D (4, —1,2) and a %3D (1,3, —2).…
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Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, -4,0), v = (-1,-1,2,2), and…
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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 1, –-2), (2, 3, 4) is O O O O
A: I have append the formula in solution part
Q: Find the magnitude of the projection of ⟨-3,-2⟩ onto the vector ⟨1,-2⟩
A: I have appended the formula used in the solution part of the question
Q: The terminal point of the vector v = i +2j +3k with initial point (4, 2, –3) is
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Q: Find the equation of the plane containing the points P = (−1, 3, 2),Q = (−5, 1, 1), and R = (6, 0,…
A: Given, The plane containing the points P = (−1, 3, 2), Q = (−5, 1, 1) andR = (6, 0, −3).
Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…
A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…
Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( 5 , −…
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Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0) Which axis on…
A: From the given points we can find two vectors and after that, using the fact that if one vector is…
Q: Show that the column vectors (1,1.2,4), (2,-1,-5,2). (1,-1,-4,0and (2,1,1.6) vectors in R are…
A: We have to prove that the given Column vectors are linearly dependent in R4.
Q: Find a vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)
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Q: Find a nonzero vector orthogonal to the plane through P(2,5, 1), Q(-3, 1, –2) and R(5, –3, –1).
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Q: Find a vector n perpendicular to the plane determined by the three points A(1, -1,2), В(2, 0, — 1)…
A: Given three points ( position vectors) are; A( 1,-1, 2) , B( 2,0,-1) and C(0, 2,1)
Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…
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Q: 2. Consider the vectors [2, 1,0, 0], [3, 1, 0, 0], [0, 0,0, 1)] in R'. Find a vector v so that v,…
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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 0, -2), (2, 3, 4) is
A: We will solve the problem
Q: Find a nonzero vector orthogonal to the plane through P(2, 5, 1), Q(-3, 1, – 2) and R(5, –3, –1).
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Q: Find two vectors of norm 1 that are orthogonal to the vectors u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2)…
A: Let X=x,y,z,t be the vector that is orthogonal to u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2) and w= (3,…
Q: Find a vector which is orthogonal to the vectors ū = (2, –2, 1) and ū = (4, 3, – 1).
A: Explanation of the answer is as follows
Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1, -2), (2, 3, 4) is
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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is O O O O
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Q: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³
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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = (5, 2,…
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Q: Consider the plane that goes through the point (4, 1, 3) I to vector (2, 3, 1).
A: It is given that the plane is passing through the point (4,1,3) and orthogonal to the vector (2,3,1)…
Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis on…
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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1,-2), (2,3, 4) is O O O O
A:
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- 5. (a) Are the vectors (1,3, 2), (2, 1,3) and (3, 2, 1) linearly independent? (b) Are the vectors (1, –3, 2), (2, 1, -3) and (-3, 2, 1) linearly independent?Find the plane through the points (7,7,5), (1,3,6) and (5,-2,-1)Q1) Find the equation of the plane passing through the point (4,-1,-5) and perpendicular to the vector <1,2,1> ; _x+_y+_z=_
- Find the equation of a plane passes through (1, 2, 3), (3, 2,1) and (-1, -2, 2) 4x - 3y + 4z = 10 4x + 3y + 4z = 10 4x +3y - 4z = 10 4x - 3y4z = 10Which vector equation below represents the line in R³ that passes through the point (-4, 5, 7) and is perpendicular to both a = and b = ? - Or(t) = 4, 5, 7> OF(t) = Or(t) = 4, 5, 7> + t 1 + t Or(t)= 4, 5, 7> + t Or(t) =Find an equation of the plane that passes through the given point and is perpendicular to the given vector or line. Point Perpendicular to x-1 (9, 2, 2) *¹ = } 4 = y + 2 = z +9 -9
- Suppose that v1 = (2,1,0,3), v2=(3, 1,5,2), v3 =(-1,0,2,1) are column vectors temporarily lying down Which of the following vectors are in span of (v1,v2,v3) ? (There are multiple correct answers) (2,3, -7,3) (0,0,0,0) (1,1,1,1)The line that passes through the point (4, –2, 0) and parallel to the vector (1, 2, -3) has symmetric equation _. Check all that applies. y + 2 x – 4 = 2 || 3 x – 1 = 4 – 2y, z = -3 6x 24 = 3y + 6 -2z - 1 y – 2 4 E- = z -2Find the vector and parametric equations of the line that passes through the points A(7,10,4), B(3,-2,2)
- Determine the vector equation of a plane that contains the line with symmetric x 3 1 equation *+-+¹_2+2 and the point P(1,3,0). = 5 4 = (1,3,0) + s(-2,5, 4) + t(3, 1,2), 5, € R | 7 = (1,3,0) + s(-2,5,4) + t(4,4,2), s, € R | 7 = (1,3,0) + s(−2,5,4) + t(1,3,0), 5,± € R none of the aboveFind the equation of the plane containing the points (0, 1, 3), (2, 2, 2) and (3, 2, 1)Find the vector, parametric, and symmetric equations for each of the following lines: (a) the line perpendicular to x+7_y_4 3 -4 with x-intercept -: the line parallel to (x, y, z) = (2, 0, -7)+t(8, -2, 12) with the same y-intercept as 3x + 5y-z = 50: (b)