For the vectors u = (-2,2, -1) and v (-2,1, 3), expressu as the sum u =p n, where p is parallel to v and n is orthogonal to v. u pn + (Type integers or simplified fractions. List the terms in the same order as they appear in the original list.)

Q: 5. Determine the value of a so that the vectors v = perpendicular. (a,3, -2) and v - (2, -2a, 1) are

A: Solve the following

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Q: For the vectors u= (-3,0,4) and v= (1,3, - 3), calculate projyu and scal, u. proj, u = OOD

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A: Now,

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Q: 2. Determine the angle, to the nearest degree, between the vectors * = (4,6,-2) and y = (1,8,2)

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A: Solution as given below:

Q: For the vectors u = -2,2,-1) and v = (- 2,1, -3), express u as the sum u = p n, where p is parallel…

A: From the given condition:

Q: For the vectors u = (-1,4) and v = (-2,2), calculate proj, u and scal,u. projyu =

A:

Q: For the vectors u = (-4, - 1, - 1) and v = (1,-3,2), expressu as the sum u = p n, where p is…

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A: Here we have, u=4,-1 and v=-4,1 ⇒u=4i-jv=-4i+j Here we have to find u=p+n  Where p=Parallel to v and…

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

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Q: For which positive value of r are the vectors (14r, 2, -1), (2, –3r², –10) orthogonal?

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Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

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Q: 9. Show that for any real numbers a and b the vectors u = ai and v = bj are orthogonal?

A: Topic:-  vector algebra

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A: Explained below

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