A free vector is Select one: O a. a directed line. O b. a directed line-segment in 3- space. c. determined by its length and direction. d. an arrow from the origin.

Q: Let Q be a point in R°. Consider a line passing through P with direction vector d.What is the…

A: Given :- Let Q be a point in ℝ3. Consider a line passing through P with direction vector d→. To…

Q: For any geometric vectors u and v, prove the following using triangle inequality. (a) ||u – v|| <…

A: a) llu-vll ≤ llull +llvll b) llull - llvll ≤ llu-vll

Q: Let u, V and w be three vectors in R. Which of the following is not defined for all u, v and w?…

A: Given u , v and w be three vectors in R3 . To find which of the following is not defined :-

Q: 4. Suppose the vectors u and w are in space R, then u - 2w and u+ 2w are perpendicular if (a) ju =…

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the…

Q: a) Find the vector that is parallel to the tanget to the circle x2 +y? = 100 at the point (3,4).

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Q: For the vector a,b,c ∈ IR3 a+b+c=0 and ===1 then ?

A: We will first assume a=(a_1,a_2,a_3),b=(b_1,b_2,b_3) and c=(c_1,c_2,c_3).Now will will use…

Q: For what values of b are the given vectors o , (smallest value)

A: Let m→=-12, b,3 and n→=b, b2,b  If m→ and n→ are orthogonal.

Q: Use the accompanying figure to write each vector listed in Exer- cises 7 and 8 as a linear…

A: Given - Use the accompanying figure to write each vector listed in Exercise 8 as a linear…

Q: Let a t b be Vnit, vectors in R Suck thent a) a-b=3, ComPute b.(24=36) let a= 43) t bcl974),Find a…

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Q: Find all values of h such that the vectors {a,, az} span R?, where a1 a2

A: Given that,

Q: The position vector of a point P is defined as the distance between the origin and the point P.…

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Q: Use the polygon law of addition to draw the resultant vector ( å + b) + ở for the following yectors.

A: The given vectors are added

Q: (d) Let u, v, w be arbitrary vectors in R³. What does the set of all combinations, Cu + c2v + C3w,…

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Q: a. Consider the following vectors in R3 V1 = Vi = |2|,v3 1 Is the set consisting of these vectors…

A: Let's find.

Q: Given that - (1, 2, 3) and - (4. 0, – 4) find the vector where %3!

A: In this question we have to find the vector z.

Q: If a = (4, 3, 1, – 2), ß =(-2, 1; 2, 3) tween a and ß. are two vectors in V(R), find the angle be-

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Q: Consider the points A (10, 9) and B (0, – 7). Find the vector AB. АВ

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Q: Under what conditions are the following true for vectors u and v in R2 or R3? (a) llu +vll = llull +…

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Q: Prove the property if a and b are vectors and m is a real number.a . b = b . a

A: Proof : let a and b are vectors and m is real number. To prove :   a . b= b . a

Q: nd the vector that has the same direction as <3, -1, 4) but has length 52.

A: First find unit vector of direction then multiply with given magnitude

Q: Determine whether given vectors spans in R? S={(2,-1,4).(3,–3,5).(1.1.3)}

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Q: Consider the following four collections {a} = C1 {a, b} = C2 {a, b, c} = C3 {a, b, c, d} = C4 %3D…

A: We have to solve given problem:

Q: Show that the vector v = ai + bj is parallel to the line bx - ay = c by establishing that the slope…

A: We first have to find the slope of the given vector and the line. If the slopes are equal then they…

Q: If å is a vector in the direction of S60°E, then draw its opposite vector and state the direction

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Q: Assume that the vectors a, b, c, and d are defined as follows: a = (8, 7) b = (6, 3) c = (2, -1) d =…

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Q: Which of the following vectors are parallel :

A: Two vectors are parallel if one can written as linear combination of other.  As showing in the hand…

Q: Let C and D be points with position vectors c and d respectively. If |c| = 5, \d| = 7 and c·d = 4,…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 2. Which polygon is the translation of polygon 1 by: (a) vector AB? (b) vector BC? 2 В 3 4 A C

A: topic - polygons

Q: Consider the graph provided find the length of the vectors u and i

A: Solution and Explanation is given below....

Q: Suppose ~u and ~w are vectors in R^n . Prove that if ~u and ~w are parallel vectors in the same…

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Q: Is the following statement correct? If A, B, C, and D are distinct nonzero vectors represented by…

A: A, B, C, and D are distinct nonzero vectors represented by arrows from the origin to the points A,…

Q: . If å is a vector in the direction of S60°E, then draw its opposite vector and state the direction.…

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Q: Given that ? = (5,4,0) ??? ? = (−1,4, −3) , find the unit vector along the direction of a vector…

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Q: 7. Write the vector w in terms of u and v, given that the terminal point of w bisects the line…

A: This question is related to vectors, we will solve it using given information.

Q: Suppose that A, B, and C are vertices of a triangle and that a, b, and c are, respectively, the…

A: Let A=(x1,y1,z1)B=(x2,y2,z2)C=(x3,y3,z3)

Q: Decide with justification if the following sets of vectors are linearly independent. (i) {2 } 3 2…

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Q: Let ā = (4, 3) and b = (– 4, 4). Find the angle between the vector, in degrees.

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Q: 2. Hhe live in Passing through He oryun and haring * l as it's divecha vector intersects the line…

A: The line in ℝ3 passes through 0 , 0 , 0 and it's directional vector is 1u3. Thus , equation of line…

Q: given the vectors from R, (-5 0 3) belongs to span{v,, V2, V3}. Select one: O True O False

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Q: Which vector is not collinear with [c, d]? O [2c, 2d] O(-c, -d] O [10c, 10d] O [d, c]

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Q: Let Q be a point in R. Consider a line passing through P with direction vector d.What is the…

A: Let Q be a point in ℝ3. A line L passes through point P with direction vector d→

Q: For what values of a is the vector (a2, a, 1) belongs to span {x1 = (1,2, 3), x2 = (1,1,1), x3 =…

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Q: Which vector is not orthogonal to ū=? a. C. b. d.

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Q: Assume that the vectors a, b, c, and d are defined as follows: a = (2, 1) b = (5, 4) c = (5, -3) d =…

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Q: Refer to the vectors u, to ug. 3. 4 1 , u2 u3 u4 Us = U6 = u7 ug Compute projs ug, where s =…

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Q: Given the triangle with vertices A=(1,2,3), B=(3,-1,0), and C=(4,1,2), find unit vector of BM, i.e.…

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Q: Consider the following four collections {a} = C1 {a, b} = C2 {a, b, c} = C3 {a, b, c, d} = C4 %3D…

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Q: Assume that the vectors a, b, c, and d are defined as follows: a = (8,3) b = (6,5) c = (4, -1) d…

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Q: Consider the lines 3 - z x – 5 l1 : 2 and I. Find two unit vectors that are parallel to l1.

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