Find the work done in moving a particle from P to Q when the magnitude and direction of the force are given by v. P(0, 0), Q(2, 3), i = (2, 5) Find PQ = Find proj. PQ Find the magnitude of the projection | |projn v|| = 'PQ Find PO- Find the work done = (hint find the dot product of the two vectors)

Q: ) Let v = (-3,6,2). Determine the unit vector parallel to v and in the same direction as V.

A: (3) Given,

Q: Find two unit vectors orthogonal to both (3, 4, 1) and (-1, 1, 0). (smaller i-value) (larger…

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Q: 4) Consider the vectors u = [3, -2] and v= [-5, 4], write a = [-24,18] as a linear combination of u…

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Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

A: Given: The vectors u =(-3, 2, 6) and v=(3,2,6) Find : The sine of the angle between the vectors u…

Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

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Q: For the vectors u = (1,1,1,2) and v= (2,-1,-3,1), (a) Find the dot product v Number (b) Find the…

A: u=(1,1,1,2)v=(2,-1,-3,1)

Q: Look at attached image, thank you

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Q: Let A=(3, 4) and B=(-1,2) be two points in R². • Find the vector v from A to B. Plot A, B, and v…

A: Given  A = 3,4  and   B = -1,2 be two points in R2.  The position vector of the point A with respect…

Q: Ben can wash a car in 2 hours while his younger brother James can do it in 3 hours. How long will it…

A: In 1 hour Ben can wash 12 part of car. in 1 hour his younger brother can wash 13 part of car.

Q: Pick any three vectors u, u, and w (e.g., u = (2,-1,2), = (-3, 4, 0), = (1, 3, 2)). Determine the…

A: Givenu→=2,-1,2=2i^-j^+2k^v→=-3,4,0=-3i^+4j^+0k^w→=1,3,2=i^+3j^+2k^

Q: ector Operations) Given vectors =, √ = and =, show (√x) = ( x )

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Q: Find a unit vector in the same direction as (2i - 6j - k). Oi-j-k O

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Q: 2. Prove the following identities related to the cross product of vectors (а) (и х у)хw — (u · w)v –…

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…