Consider the two vectors in R3: ü = (-20, -20, -12) and = (-25, c, -15) where c is an unknown. (a) For what value of c are ü and i collinear? Answer. c = Number (b) For what value of e are i and v orthogonal? Answer. c = Number FORMATTING: Give exact answers, not decimal approximations. To enter fractions like , type 1/2.

Q: Determine the angle between the given vectors. (а) а — 3і — 2ј, b %3 2i + 2j

A: a→=3i - 2jb→=2i + 2j

Q: Given the vectors u = (-3, 1, 2), v = (1, 2, 1), and w = u + mv, determine the value of m so that…

A: The given vectors are u=-3,1,2,v=1,2,1 and w=u+mv. We have to find the value of m.

Q: Consider the vectors v, = (1 0) and v, = (0 1) in R,. the vector ( 0.4 3.7) can be written as a…

A: Linear combination

Q: Compute the indicated vectors and also show how the results can be obtained geometrically. b-c

A: Given: b=23, c=-23

Q: . Compute the dot product of the given vectors and find the angle between them: a) u = (3,7,-2) and…

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Q: Determine the dot product of vectors a, b when |a| = 5, |b| = 1 and the angle between a and b is…

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Q: given two vectors v m which are perpendicular. under which condition is V+W perpendicular to V-W?

A: Since vectors v and w are perpendicular so, their dot product is 0

Q: Determine the magnitude of the resultant of the given vectors. Then give the direction of the…

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Q: 3 Give the position vectors of A, B, C, D and E relative to O for the diagram below. B D-

A: In geometry a position vector so known as location vector. Here we find position vector relative to…

Q: 13. Show that the pair of vectors i + i and i – i is perpendicular.

A: Two vectors is said to be perpendicular if their scalar product is zero.

Q: Find the magnitude of the given vector. (2, 6, –2)

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Q: Find the measure of the smallest nonnegative angle between the two vectors. Round approximate…

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Q: 1. Assume the lengths of the vectors 2a – b and a + 3b , assuming a = (2,1,3) and b = (-1,2,2)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Is it true that if vectors a-b and a+b are orthogonal, then la|=|b|.

A: Given vectors a-b and a+b are orthogonal. The objective is to prove if vectors a-b and a+b are…

Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 15i – 6j, V = 4i +…

A: Given, Vector U = 15i -6j        U = 152 +(-6)2 = 225+36 = 261 = 16.2 Vector V = 4i +13j         V =…

Q: Find the magnitude of the vector AB A=(4, 1) and B=(-3,0)

A: Given that, A = (4, 1) B = (-3, 0) We have to find the magnitude of the vector AB.

Q: In the accompanying figure, it looks as if v1 + v2 and v1 - v2 are orthogonal. Is this mere…

A: Given figure shown below.

Q: Find the measure of the angle between the two vectors. 1) u = (4, 9) v=(-3, -8) 2) u = (-8, 9) v =…

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Q: Given two vectors e1=(1, 0, 0)T and e3=(0, 0, 1)T in the 3D space, figure out b) e1-e3

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Q: The angle between the two vectors u = (4, 7) and v = (11 /2, 3 /2) computed via the cosine formula…

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Q: Find the measure of the angle between the two vectors. 4) u =(-6, -2) v = (6,-6)

A: An angle between 2 vectors is defined as, cosθ=u→·v→|u→||v→|   Here given vectors are,…

Q: Given v=[2,-9] and w = [7,-8], what is 2w-v written as a linear combination of unit vectors?  please…

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Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 14i + 6j, V = -13i…

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Q: Find the dot product for the pair of vectors. i+ 4j, 7i - j O -3 3 11 Question 13 (1 point) Listen…

A: FIND THE VECTOR DOT PRODUCT AND ANGLE BETWEEN TWO VECTORS

Q: Find the value of a so that vectors U = ai + 6j and V 5= 9i + 12j are perpen dicular.

A: Our Aim is to find the value of a so that the vectors U=ai^+6j^ and V=9i^+12j^ are perpendicular.

Q: Find the angle between the given vectors to the nearest tenth of a degree. = (8, 6) u = (7, 8), v =…

A: Topic:- vector algebra

Q: Given the vectors a=(1,2,3) and b=(1,−1,2), what is the dot product a⋅b⋅a?

A: Solution :- let a = (x1, y1, z1) and    b = (x2, y2, z2)  be any two vectors then their dot product…

Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated…

A: To determine the value of b.

Q: Given two vectors a = (−2, 1, 3) and b = (3, −1, 2), does c = (−18, 7, 1) lie on the plane…

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Q: -) THREE VECTORS A, B, AND C ARE RELATED AS FOLLOWS ! A AT 180°, A +C =-5+j15, 2 C = CONJU GATE OF…

A: Solution :-

Q: 1. Given three vectors u =(1,–3,0), v=(2,1,–1) and w=(0,2,3). Determine: a. Bu + 4v – Sw]. b. Cosine…

A: 1. a.

Q: 2. Determine the value of c, so the given vectors are perpendicular: u=[-4c, 3], v = [-1, 2]

A: L

Q: 1. (a) Calculate the dot product of the two vectors (b*) Find the value for c for which 2 and [2] C…

A: Calculating the dot product of two vectors

Q: Find the angle between the vectors. 20 u= - 5 531-Si and v= zi-[2 V3= 2i:

A: The given vectors are

Q: If A= (3/2) i –(½) j + k and B= i+j+2k, what is the value of A x B? Are the vectors orthogonal? O…

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Q: Let a = (-1; 3; 2) and b = (4; -2; 1). (b) Find two unit vectors orthogonal to both a and b. Are…

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Q: 2) With respect to the origin 0, the position vectors of points A, B, Cand D are given by OA = 1 OB…

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Q: For what value of "c" are the following vectors perpendicular? 3 (2, с, 9) аnd ў 3 (Зс, —1,5) (Зс, —…

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Q: Consider the vectors a = 4 i+ 8 j-8k, b = 2 i +k and c = 4 j-5k. Are the vectors a and b+c…

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Q: Express the given vector in terms of the unit vectors i, j, and k. (14, 0, 4)

A: Given,  Vector < 14, 0, 4>

Q: Find the sauare of the magnitude of the vector w =u + 2v if u = (8, 2,0) and V = (-1, 1, 2) |wf =…

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Q: If A = 3i + 4j and B = 7i + 24j, the %3D vector having the same magnitude as B and parallel to A is…

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Q: Find two unit vectors that are orthogonal to both u = -7i+ 3j + k, and v= 2i + 4k

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Q: If a = 2i – j+k and b = 2j – k, for which value of t are the vectors a + tb and a orthogonal? 6 2 -3

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Q: Find a vector B for which that is parallel to A =-6i +3j –2k but has the opposite direction.

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Q: Two orthogonal unit vectors x, y E R° such that ||æ – y|| = 2.

A: See the attachment

Q: Find the angle between the vectors u = - 5i – 3j and v = 6i + 2j + 5k.

A:

Q: One of the components of cross ultiplication of the vectors A = 21 + 3 *:j + 4k and B = i-2j+3k is…

A: Given vectors are A=2i+3j+4k and B=i-2j+3k. Cross multiplication of given vectors is:…