Let u and v be two orthogonal unit vectors in R. We have a triangle ABC in R' such that AB = 2u – 6v, BC = ủ + 7v, CA= - :-3u- v. Find the angles of the triangle A BC.

Q: u and i are vectors of R" such that ||ū|| = 3, |||| = 4 and the angle between them is. Determine the…

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Q: Express the vector in terms of the unit vectors i and j. 2(3, 3) + 3(4, 2)

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Q: Find the angle 0 between the vectors. u = (1, 1, 1), v = (7, -6, 5), (u, v) = u1Vı + 2u2v2 + U3v3…

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Q: Compute the angle between the vectors u = [2, 1, -2] and v = [1, 1, 1].

A: To find out the angle between two vector use the formula. First find dot product of these two…

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (12, -16, -2)

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Q: Find the angle (in radians) between the 2 vectors U(-3, 4, -4) and V(1, 2, 2)

A: Given vectors are,               U(-3, 4,-4 ) and V(1, 2, 2 )

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: Determine the two unit vectors that are orthogonal to v = (1,2). Which two unit vectors are parallel…

A: Let the required unit vector orthogonal to v be <x,y>

Q: Find the angle 0 between the vectors. u- (3, 2, 0), v = (-2, 3, 4) radians

A: u=3, 2, 0  &  v=-2, 3, 4 Now, u·v=3-2+23+04=0 Now the magnitudes is,…

Q: Find the angle between the vectors a=(2,2,-1) and b=(5,-2,3)

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Q: Find the cross products u x v and v xu for the vectors u = (4,4,0) and v = (0,2, - 5).

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Q: Let the vector 3i +j can be expressed as a sum of vectors u and v where u is parallel to the vector…

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Q: Find the angle θ between the two vectors.u = (3, 3), v = (−2, 2)

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Q: is The unit vector in the direction of v=(4,0,–3)

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Q: What is the angle measure between the vectors u = (-5, 8) and v = (3, 9)?

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Q: The unit vectors normal to the vectors (2, - 8,11) and (- 3,0,5) are

A: Find unit vector

Q: Find two unit vectors orthogonal to both v (1,1,-1) and w-(2,-1,1).

A: Calculation:Compute the two unit vectors as follows.

Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

Q: Find a unit vector perpendicular to plane PQR determined by the points P(-3, 3, -4), Q(4, -1, - 23),…

A: Given query is to find unit vector perpendicular to PQR.

Q: For the vectors u= ,0,2) and v= ,- 3), calculate projyu and scal, u. projy u = O DD

A: Given ,the vectors u=-4,0,2  and   v=1,3,-3

Q: The vector from the origin to point A is given as (-2, -4, 5) and the unit vector directed from the…

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Q: Consider the vectors u = (7,1,5, -5) and i = (3,4, c,0) in R*. a. Find the value of c that will make…

A: In this question, the concept of scalar products is applied. Given, u→=7,1,5,-5 and v→=3,4,c,0 in R4

Q: ind the cross products u×v and v×u for the vectors u=2,4,0 and v=0,3,−

A: To find the cross products u×v and v×u for the vectors u= (2,4,0) and v=(0,3,−6).

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (3, 2, −1), v = (1, 2,…

A: Now,

Q: 1. Express A = (3, 1, –1) as B+ C, where B is parallel to the vector (1, 4, 2) and C is…

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Q: Express A = (3, 1, – 1) as B+ C, where B is parallel to the vector (1,4, 2) and C is perpendicular…

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Q: Find the angle θ between the vectors.u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

A: The given vectors are, u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

Q: 19. Show that the pair of vectors 8i+j and i-8j is perpendicular.

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Q: Two vectors u, v in Rº have lengths 4 and 4, respectively. It is also true that u- v = 0. What is…

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Q: Find the angle between the vectors u and v if u = (2,3,5) and v = = (1,–4,3) in

A: First we convert this into vector then find the angle

Q: Find two independent vectors both of which are perpendicular to i = 3

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Q: Use the vectors u = (6, 6) and v = (-9, 3) to find the indicated quantity. (u - v)v (u · v)v =

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Q: Compute the angle between the vectors u = [2,1, -2] and v = [1, 1,1].

A: Given: u=21-2   and   v=111 Formula Used: cosθ=u.vuv

Q: Find the angle θ between the two vectors.u = (10, −5, 15), v = (−2, 1, −3)

A: The given vectors are To find the angle between the given vectors, use the formula

Q: For the vectors u = (- 3,5) and v = (- 5,2), calculate proj,u and scal,u.

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Q: 10. Which of the vectors U =, V = and W = are in the same plane?

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Q: Find a unit vector which is perpendicular to both đ = (1, 1, 0) and b = (-2, 3, 0) Answer:

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Q: If u is a unit vector find the dot product of vectors u and w

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Q: Find the angle between vectors v = (1,2,3) and w = (2 -1, 4)

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Q: Find the angle θ between the vectors.u = (3, 4), v = (5, −12), ⟨u, v⟩ = u ∙ v

A: Given vector: Formula used : By dot product equation:

Q: Find the angle θ between the vectors.u = (0, 1, 0, 1), v = (3, 3, 3, 3)

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Q: Find the two unit vectors orthogonal to both a = 3j + 2k and b = -i- 2k. O A -61 - 2j + 3k and 6i+…

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Q: 2. (a) Compute ||(1,2, 3)||- (b) Find the angle between the vectors (1, v3) and (1,0).

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Q: Find the angle θ between the vectors.u = (−4, 1), v = (5, 0)

A: u = (−4, 1), v = (5, 0)

Q: Let u and v be vectors. If their dot product is zero what is the angle between u and v (in degrees)?

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Q: Find the angle θ between the vectors.u = (2, 3, 1), v = (−3, 2, 0)

A: Given: u=2,3,1, v=-3,2,0 we know that angle θ between two given vectors A=x1i+y1j+z1k, B=x2i+y2j+z2k…

Q: Find the angle between the vectors u and v if u (2,3,5) and v = : (1,–4,3) in (Ctrl) ►

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Q: Let the vectors (2,3) and (-6,4) be    Your point product is: ? The angle between the vectors is:…

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Q: The distance between vectors v1 = (2, 1, -4) and v2 = (1, -1, -2) equals: Select one: O a. -2 O b. 3…

A: To find The distance between the two vectors v1=(2,1,-4) and v2=(1,-1,-2)

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (10, -12, -2) %3D V =

A: Find the unit vector that is orthogonal to both u and v