Let a =< -5, 2, 1 > and b =< -3, -4, 3 >. Show that there are scalars s and t so that sa + tb =< -7, -18, 11 >. You might want to sketch the vectors to get some intuition. S = t =

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A: This question can be solved using the concept of finding the vector joining two points and dot…

Q: Find the value of x so that the vector i+2j+xk   makes and angle  pi/4  of  with the positive…

A: i+2j+xkTo Find: Value of x so that the vector makes an angle of π4 with the positive z axis.

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 ||e − 4f||, assuming that e and f are unit vectors such that ||e + f|| = √3.

A: The step-by-step solution to the given question is ..  we have ,  e+f=3..........(1) we have to find…

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Q: [:] [] Find c so that the vectors and are parallel.

A: Find c so that the vectors c4 and 25  are parallel. Let u=c4 and v= 25 be two vectors. Two vectors…

Q: Let a = (-4, 5, -1) and b = (0, –3, 2). Show that there are scalars | | s and t so that sa + tb =…

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Q: 3. Find the following unit vectors: a. aCD in RCS b. aDE in CCS C. aEC in SCS

A: aCD in RCS is to be calculated: Converting D from CCS to RCS xD=5cos π=-5yD=5 sin π=0zD=-12 Hence,…

Q: Suppose that the vectors below have the following components: a = b= č = What is the exact value of

A: We have to find the exact value of the given vector multiplication.

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Q: Sketch the following vectors, and find their components andlengths: i + j + k

A: The vector is i+j+k sketch the vector and find its length.

Q: Let a = and b =. Show that there are scalars and t so that sa + tb =. You might want to sketch the…

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Q: Find the cosine of the angle between the vectors with respect to the standard inner product on P2.…

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Q: latél Show that if a is perpendicular to each of the vectors and then a is perpendicular to 26 +4

A: The detail solution is given below

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Q: Find cos 0, where 0 is the angle between two vectors a = 2i – 3j + 2k, b = -2i + 2j+6k

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Q: (B): Find the unit vector perpendicular to the vectors: 31-4/+5k ; 11+5/-6k dw (C): If w = tan x and…

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Q: Consider the graph provided find the length of the vectors u and i

A: Solution and Explanation is given below....

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Q: Find the following for the vectors

A: Given that: v=-9i+ju=-5i+7j     NOTE: As per our answering guidelines, we can only answer 1 question…

Q: Given the vectors A = 3i – 5j + 2k and B = 7i + j – 2k. Find the vector projection of A onto B.

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Q: If a and b are vectors with the same initial point and angle between them, prove that||a - b||2 =…

A: Consider the given expression as, a-b2

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Q: Find the angles between the vectors to the nearesthundredth of a radian. u = √3i - 7j, v = √3i + j -…

A: Given:u=3i-7jv=3i+j-2kAngle:cosθ=u→.v→u→.v→

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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: Let a = (5, 4) and b = (1, –5). Show that there are scalars s and t so that sa + tb = (-13,-22) You…

A: Given, Let a=5,4,b=1,-5 And sa+tb=-13,-22

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A: Find the unit vector in the direction of the given vector a . vector a = 20i - 21j  . Here i…

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A: Givena→=⟨4,−3,−4⟩

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Q: (b) Find a vector i that is parallel to ↑ and perpendicular to L.

A: As per your demand, we solve part b) only

Q: Find a unit vector that is orthogonal to both ı̂ +ȷ̂  and ı̂ +?̂

A: Given query is to find the unit orthogonal vector to the given vectors.

Q: Let a = (4, 5) and b = (2, –2). Show that there are scalars s and t so that sa + tb = (2, – 20) You…

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Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a - b)…

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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: (B): Find the unit vector perpendicular to the vectors: 31-4/+5k 41 +5/-6k i (C): If w = tan x and…

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Q: Find a so that the vectors v=i- aj and w = 7i- 10j are orthogonal. (Type an integer or a simplified…

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Q: 2. Find the angle between the following two vectors. and

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Q: Express the vectors in terms of their lengths anddirections. i + 2j - k

A: Given:  i + 2j - k

Q: Let ā = . Find a unit vector in the direction of a

A: For any vector a→, the unit vector in the direction of  a→ is a→a.

Q: Let a = and b =. Show that there are scalars s and t so that sa + tb =. You might want to sketch the…

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Q: Let a = and b =. Show that there are scalars s and t so that sa + tb =. You might want to sketch the…

A: a=-2, -1, 0b=-4, 1, 3sa+tb=s-2, -1, 0+t-4, 1, 3=2, 4, 3-2s-4t=-2s+2t=1 ...(1)-s+t=4 ...(2)3t=3…

Q: Find the angle between the vectors i – k and 4i + 4j -2k

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