Find the direction cosines of u and demonstrate that the sum of the squares of the direction cosines is 1. = (a, b, c) cos(a) = cos(B) = cos(y) =

Q: 12 If the position vectors of P and Q are i+3j- 7k and 5i - 2j + 4k respectively, find PQ and…

A: Since,you have posted multiple questions so according to our guidelines we will solve only first…

Q: Find the angles between the vectors to the nearesthundredth of a radian. u = 2i + j, v = i + 2j - k

A: Now,

Q: The vectors A 5i + 7j – 8k and B 3i + yj + zk are known to be parallel. Find y and 2 y = = Z

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Q: Let 0 be the angle between the vectors u = 2i + 3j - 6k and v = 2i + 3j + 6k a. Use the dot product…

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Q: Find the component form of the vector.The unit vector that makes an angle u = -3pi/4 with the…

A: Given: The unit vector that makes an angle  To find: The component form of the unit vector.

Q: If the position vectors of P and Q are i + 3j- 7k and 5i- 2j+ 4k respectively, find PQ and determine…

A: The equation of the line, PQ passing through the points P and Q is defined as follows.…

Q: Find the direction cosines of u and demonstrate that the sum of the squares of the direction cosines…

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Q: Find the cosine of the angle between the vectors: a = 4i + 2j-k b=2i+ 4j-k

A: Simply take the dot/scalar product of both vectors a & b.

Q: Find the angle θ between the vectors a=5i−j−4k and b=2i+j−4k. Answer (in radians)

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Q: Find the angles between the vectors to the nearesthundredth of a radian. u = 2i - 2j + k, v = 3i +…

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Q: Find the angle θ between the vectors (a) in radians and (b) in degrees.

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Q: Find the angle between the vectors u = ⟨3, 1⟩, v = ⟨2, −1⟩     (a) in radians and (b) in degrees.

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Q: Find the angle between the vectors a = 10i – j – 5k - and b = 2i+j – 4k. Answer (in radians): 0 =

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Q: α, β and γ are the angles made by the vector with x, y and z axis respectively. The squares of the…

A: Given ,  α, β and γ are the angles made by the vector with x, y and z axisrespectively. We have to…

Q: Explain how you might use the dot product of cos(B – a). two vectors to derive a formula for…

A: Here the objective is to derive the formula for Using the dot product of two vectors.

Q: Find the component form of the unit vector that makes an angle 0 = 3 2л with the positive x-axis.

A: We have to write the component form of the unit vector which makes an angle -2π/3 with positive x…

Q: Find the angle 0 between the vectors in radians and in degrees. u = 9i + 8j + k v = 8i - 9j (a)…

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

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Q: Find the angle 0 between the vectors in radians and in degrees. - co) + sin() = cos 4 u = cos i +…

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Q: 12. If the position vectors of P and Q are i + 3j-7k and 5i- 2j + 4k respectively, find PQ and…

A: NOTE: Hi! Thank you for your question. As per the honor code we are allowed to answer one question…

Q: -2i -sj+si and -i+zi are orthogonal, then

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Q: Let v = (1, 1, 1) and w = (6, -5, 10). Find the cosine of the angle 0 between the vectors v and w.…

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Q: Find the angle e (in radians) between the vectors. co()i - sin(); u = cos 4 v = cos i + sin 4 4 e =…

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Q: Find cos(0) if 0 is the angle between the vectors u= 4i – 3k and v = 2i – 2j + k 2 14 15 15

A: First I have written a short note , just use them and find that  Answer is 1/3

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A: Given the unit vectors v, w  we have to prove :- cosα-β = cos α cosβ+sin α sin β α = the angle…

Q: 3. Find the angles a, ß,y, which the vector Á = 3î – 6î + 2k makes with the coordinates axes and…

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Q: . Find the angle between the vectors å = 4i – 35 + k and b = 21 – k. (First find an exact expression…

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Q: Find the angle between the vectors u = 2i − 3j + k, v = i − 2j + k (a) in radians and (b) in…

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Q: Find the angle between the vectors u = cos( /6)i + sin( /6)j, v = cos( 3/4 )i + sin(3/4 )j     (a)…

A: u=cosπ6i+sinπ6j,  v=cos3π4i+sin3π4j Now,…

Q: The vector êr and êe in terms of î and ĵ is given by êr = î cos e + ĵ sin 0, %3D and êe = -î sin 0 +…

A: True

Q: Find the direction cosines and direction angles of the vector 3i +2 i – k .

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Q: Let v = (1, 1, 1) and w = (6, -5, 10). Find the cosine of the angle e between the vectors v and w.…

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Q: Let i = 3i – 13j +k and j = 13i + 3j+ 5k be the two vectors. Find the angle (in radians) between the…

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Q: Find the vector v that has magnitude 3| and makes the angle 0 = n with the positive x-axis. v = help…

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Q: Find the angle between u=3i+2j and v=-4i

A: Given,          The two vectors are u=3i+2j and v=-4i.

Q: Find the angle 0 between the vectors in radians and in degrees. u = 4i + 2j + k v = 2i – 4j (a)…

A: u=4i+2j+kv=2i-4j

Q: The angle between the vectors A = 2j -3j +1k and B = 4i -3j +1k, in term of cos@ is !!

A: We use the definition of angle between two vectors to find the angle between the vectors A and B.

Q: Find the angle e between the vectors. -(cos , sin 2), v- (cos , sin. x radians

A: Given that, u=cos3π4,sin3π4 and v=cosπ6,sinπ6. It is known that, the formula for u·v=u·v·cosθ.…

Q: nd the an

A: Here we have, u→=cosπ3i+sinπ3j ........................................ (1)  v→=cos3π4i+sin3π4j…

Q: Find the angle between the given vectors to the nearest tenth of a degree. U = 13i - 4j, V = 2i +…

A: For two vectors a and b we know that their do product is a·b=abcosθthen cosθ=a·bab…

Q: Find the position vector of the point of intersection of the line joining the points whose position…

A: Given: The position vector of the points 5i^-4j^ and -3i^+4j^; -13i^+4j^ and -5i^+j^

Q: Find the angle 0 between the vectors. (c0 ST, sin S), v- (cos , sin ) 5Tt 4 COS 3 COS 4 radians

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Q: 1. Find the angle that the vector V = makes with the positive x axis.

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Q: Find the component form of the vector v if ||v|| = 5 and when drawn in the standard position v ties…

A: Given: ||v|| = 5  θ=45∘

Q: Find the angle 6 between the vectors. u- (1, 1, 1), v- (5, -4, 3), radians

A: Angle between the two vectors can be found by applying dot product of two vectors.

Q: Find a vector v whose magnitude is 6 and whose component in tho i direction is twico the component…

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Q: Show that the points with position vectors 3i–5j, 4¿+j, 6¿+13j are collinear. If the point whose…

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Q: The vectors i = (-4, p, –2) and j = (-2,3, 6) are such that the angle 0 between them satisfy…

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Q: Find the angle 0 between the vectors in radians and in degrees. u = 6i + 4j + k v = 4i – 6j (a)…

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Q: Find the angle 0 between the vectors in radians and in degrees. u = 7i + 2j + k v = 2i – 7j (a)…

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