The edges OP.0Q and OR of a tetrahedron OPQR are vectors p, q and r, respectively, where p = 21 + 4j, q 2i j+ 3k and r = 4i - 2j + 5k. Show that OP is perpendicular to the plane containing OQR.
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- Two vectors A = 1î - 2j and B = 2î + 3j. Find the approximate angle between the vectors (-3A) and (2B)? %3D A. 60 В. 30° O C. None D. 75° E. 120°Find the angle between vectors A = i- j + 2k and B = 3i + 2j +4k. A. COS-1 √58 3 B. Cos-158 3 58 √√3 58 √√3 OC. cos 1. D. cos-10199 igs 0199 ۹ 5۱۹ من Example 2; find O between A¯and B? A*=2î +3ƒ +k , B =3î -2j +k Example 3; if 0=30o between A¯and B'find q value? A¯=2î +2j +4k , B'=qî +j -2k Example 4; Find the angle between the vectors A¯=2î +3ƒ +1k , B` =-4î +2ƒ -1k طلاب ممكن أحد يحل ذني دعاء صاحب حسین 7:56p äclul 21.02.05 >
- 44 8) PIT F12 26 Prt Sc % 3 5 8. W Hint 1 E For vectors B = – 22 – 6ŷ and A - 5a - 4ý calculate: a. Ā + B = A + B %3D Direction in degrees relative to +x- axis: b. А - В — Ã – B %3D axis: Direction in degrees relative to +x-O/14 المحاضرة الأولی..0980ba1 Cross (Vector) Product: The cross product of the vectors a and b is witten as a x b |(a cross b) The result of the cross product is a vector. ie. vector × vector = vector For two vectors a = a,l+a;] + a;k and b = bjl+ b;] + b,k the cross product is calculated as follows: axb = (a,b, – a,b,)1– (a,b; -a,b;)) + (a,b; - a,b,)k This looks like a complicated formula to remember but there is an easy way to do the cross product using a matrix. Example (4): a = 2î + 4j + 3k b = i + 5j – 2k calculate a x b Solve: a Xb = 3 -2 axb = X-2) - -rh il-8-6) -3(-4-3) + Â (lo -4) Google Ad IIIf A C -12.2, A 31-43, and C = 6.5, the angle between the two vectors when they are drawn starting from the same point is Select one: a. 112° O b. 122° С. 1020 d. 92°
- Given the following three vectors: A=-9î+7), B = -61 -107 and vector C has a magnitude of, ||=9 and makes and angle of 0 = 297° Determine: c) Find the dot product of vectors A and B. d) Find the cross product between vectors B and C.4. Vectors A,B and C form a triangle, as shown in the figure. Prove the law of cosines, |CP = |A|? + \B|? - 2 |A||B| cos a using the given vector triangle. The interior angle between A and B is a. BThe magnitude of two displacement vectors are d and 2d, and themagnitude of the total displacement is also d √3 . What is the anglebetween these two displacement vectors?a.3π/4b. π/4c. 2π/3d. π/2
- tion The angle between the vectors Á = 21-1/+4k and B= 41 -3j+1 k, in term of cose is %3D Answer: put of NEXT ENG f2 f3 14 f5 f6 米 2. 3. 4. 6. 01 00 LO 96 %24 %23620A%20%3D%20(-4.0%2C%201.0%2C%202.0)%20y%20B%20%3D%20(1.0%2C%20-... INGLÉS ESPAÑOL FRANCÉS Determine if the vectors A = (-4.0, 1.0, 2.0) and B = (1.0, - 2.0, 3.0) are parallel to each other. (You must do the mathematical calculation, and indicate whether they are parallel or not.) Enviar erdado ContribuirAcademic Departments ETC - CIMS The components of vector A'are given as follows: Ax = 5.6 Ay = -4.7. What is the angle between vector A'and positive direction of x- axis? a. 127° O b. 90° O c. -40° O d. +40° If the magnitude of the vector product of two vectors a and b are are equal to 0, then what do we know about a and b? O a. they are in different planes O b. they are perpendicular they are in different directions d. They are parallel