Find the direction cosines of u and demonstrate that the sum of the squares of the direction cosines is 1. u = i + 2j + 2k cos(a) cos(ß) = cos(y) =

Q: Find the length of the vectors (a) 2i⃗ +3j⃗ −k⃗

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

Q: Use the given vectors u = 5i-4j to find u. W W = -2i - j

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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: The vector with length 4 and direction k is Di+Di+ j+ k.

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Q: PQRS is a parallelogram and X is on the side QR. If vector PQ=3i+j, and  vector XQ=2i+j. find PX.

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Q: Find the length and direction (when defined) of u×v and v ×u. u = 7i- 2j - 8k, v=8i – 8k

A: length

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

A: Consider the two vectors. u=2i+2j-k and v=3i+4k It is given that θ is the angle between the vectors.…

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: Solution: we know that u→=ucosθ i +usinθ j

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

A: we find direction cosine with x, y and z axis..

Q: The angle between u = 3i -j-k and v = -7i – 2j + 4k is

A: u=3i-j-k and v=-7i-2j+4k The formula for angle formed between two angle is, cosθ=a·ba·b

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: This is a question of vector algebra. Kindly see the uploaded answer for detailed solution

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

A: Sum of square of direction cosine is equal to 1

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

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

A: Given,           u=4i+3k           v=2i-2j+k

Q: is the unit cube having one corner at the origin and the coordinate planes for three of its adjacent…

A: Given cube of unit length the co-ordinates of points are.A→→(0,0,1)B→→(1,0,0)C→→(1,1,0)D→→(0,1,0)

Q: Given vector a= i+ 2j and b= 2i + 5j. Let 0 be the angle between the vector's directions. Compute…

A: Consider the given vector a→=i+2jb→=2i+5j   Find the magnitude. a→=12+22=1+4=5   b→=22+52=4+25=29

Q: In a triangle ABC, points E and F are on the sides AC and BC respectively, such that AE is 1/3 of AC…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

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

A: cosθ=u.vuv

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

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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: 2. The angle e between the vectors u and v satisfies cos 0 = So if u and v are perpendicular, then…

A: The angle between two vectors is, cosθ=u·vu v The vectors are perpendicular if u·v=0. The given…

Q: Suppose the vector t has magnitude 48 and makes an angle of 239° with the positive x-axis (measured…

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Q: The vectors A 6i + 4j – 8k and B = xi + 6j + zk are known to be parallel. Find x and z x = 9. -12

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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

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: 7. Find the angle betweenu and v. u = 6i and v = 5i+ 4j

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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 angle in degrees between u = (1, 2, 0) and v = (1, -2, 1)

A: Given, u=1,2,0v=1,-2,1 The formula for finding the angle between the two vector is, cosθ=u→·v→u→v→

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

A: For two vectors u→, v→ in 3-space we have that:                     u→·v→=u→ v→cos θ⇒cos θ=u→·v→u→…

Q: 4. For the vectors (2, 1) and = (1, 2) Find the dot product u · v, and the angle 0 between the two…

A: According to the given information, it is required to calculate the dot product and angle between…

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

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

Q: Let u = 3j - 2k and v = 2i + 5k. Calculate cose where between u and v. is the angle

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: topic - vectors

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: Given that, ‖u‖=2,  θu=5‖v‖=1,  θv=2 The objective is to find the component form of  u+v.

Q: 2. For the vectors (1, 1) and =(-1,1) Find the dot product u · v, and the angle 0 between the two…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: Let's find.

Q: 7. For the vectors = 8i + 2j and v = 5i – j Find the dot product u · v, and the angle 0 between the…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

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Q: If the position vector of a particle P is r(r) (3cos t,5sin7,4 cos t) a) Show that the speed of the…

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Q: In many applications, the angle 0 between vectors play an important role; usually in the form of…

A: We will find out the required value.

Q: In the diagram below, a and b are vectors such thay cos0 = 1/6. Given thay a= i +j+ pk and b= 2i…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: This question is based on vectors.

Q: Find the angles that vector D 2.5 - 8.5 + k) m makes with the x-, y-, and z- axes.

A: Follow the procedure given below.

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: To find the component form of u+v

Q: Find the angle 0 between the given vectors to the nearest tenth of a degree: u = 13î – 8î and 3 = 2î…

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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: (i) Find the direction cosines for v = 2, 3, 4 .  (ii) Verify that the sum of their squares equals…

A: We know that If the vector is xi+yj+zk=(x,y,z) and  r=length of x,y,z =√(x2+y2+z2) Then the…