Problem 1: For the two vectors A = x -2ŷ - 2 and B = 2x + y − 32, find (a) A- B, (b (A - B). (A + B), (c) (A - B) × (A + B), and (d) the angle between A and B.

Q: Let a = 2 (-) (-3). 1 and b = What is a|²|b²+ la · b|²? -2 be two vectors.

A:

Q: Find values of a and b, for which the following vectors are parallel: (8, a + b, 6), v = (4, 3, 2a —…

A: Given:   u = ⟨ 8 , a+b , 6 ⟩     v = ⟨ 4 , 3 , 2a - b ⟩

Q: If A = 4a, - 6a, + a, and B = 2a, + 5a,, find: (a) A B +2|B (b) a unit vector perpendicular to both…

A:

Q: For the given vectors: å = (-2,-3), 5 = (1,–2), 7 = (0,3), find: (a) 2å – 35 + ở (b) angle between…

A: Given the vectors a,b and c. The solution to the given questions are as follows.

Q: Determine the dot product for the two vectors: x = ai+bj+ck and y = di+ej+fk where a = 4, b = 5, c =…

A: Given,

Q: = [21] and v₂ = [-]₁ (a) Give an example of three vectors that are linear combinations of v₁ and v2.…

A:

Q: The initial and terminal points of a vector v are given. Terminal Initial Point Point (2/²) (14) (a)…

A:

Q: For the given vectors a and b, find the cross product a x b. (2, 0, -3), b = (2, 1, 0) a x b = %3D

A:

Q: See the points D(4,-2,5), E(-1,3,5), and J(4 + 2√3, −2 − 2√3, 5+ 2√2), and the line / with symmetric…

A:

Q: For what value of (a) will the vectors V=-4i-8j+ak, U=2i+4j-5k are parallel?

A:

Q: Let be two vectors, such that a=(3î+2j-2k) cm and b=(2î+2ƒ+k) cm, calculate: (A) C²=3(a¹·b¹)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: .If A = 2a, + a, - 3a, and B = 4ax + 2a, – 3a, are vectors, find (a) A· B (b) Á xB (c) Angle between…

A:

Q: Find the angle between vectors: a = 51-4j+2k and, b= 41+3)+2√5k

A:

Q: For the given vectors: å = (0,3), b = (4, –2), ở = (3,2), find: (a) 3å – 6+ 2č (b) angle between the…

A:

Q: Given the following vectors A = -4a +3a-2a₂ X y B=a_+5a +7a_ X y z C=-2a-4a +6а X y Evaluate |AX…

A:

Q: In the figure to the​ right, it looks as if v1+v2 and v1−v2 are orthogonal. Under what circumstances…

A:

Q: Find C, the length of C, which is the sum of A and B.(Figure 2) Express your answer in terms of A,…

A: Consider length of vectors A, B and C is A, B and C.By linear pair  θ +c =180° c= 180- θ

Q: Given the vectors, a = (4,-5) and b = -10i -8j: %3D a. Find a - 2b.

A:

Q: Given the vectors a = (−2, −5, −3) and b = (1, −4, 2), find 1.  5a − 1/3 b. 2. The length of a.

A:

Q: For the given vectors: a = (2,–3), b = (0,3), c = (1,4), find: (a) 3å – 6+ 2č (b) angle between the…

A: a) this is the case of scalar multiplication and then addition and subtraction. So 3 times of vector…

Q: If a, b and c are three non-coplanar vectors, then find the value of a.(bxc) b.(cxa) c.(bxa) +…

A: Use the properties of vector box product as follows: a→.(b→×c→)=[a→ b→ c→]=[b→ c→ a→]=[c→ a→…

Q: See the points D(4,-2,5), E(-1,3,5), and J(4 + 2√3, −2 − 2√3, 5+ 2√2), and the line / with symme…

A:

Q: For the given vectors: å = (-3, –3), B = (1,–2), ở = (1,3), find: (a) 2å – 35 +ở (b) angle between…

A: