Use the dot product to find the angle between the vectors v =i – 2j + k and w = i+j-2k. For which valuc of x are v =< 1,3, 5 > and w =< 3, x, –1> orthogonal?

Q: u = (1,2, 0), v = (-1,4, 1)

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Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

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Q: Use the cross product to determine the angle between the vectors [4, 5, 2] and= [-2, 6, 1]. Verify 9…

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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: Find the angle between vectors a= (-/2, 0, v2) and b = (-1,1,0). %3D

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Q: 2. Consider the two vectors in R³ with components u = (2,-1,-1) and v = (-2,1+ √√3,1-√3). (a) (12…

A: Step 1: Step 2: Step 3: Step 4:

Q: v = {3,k,-2} and w = {-2,1,2k} What value(s) of k are the vectors v and w perpendicular?

A: To determine the value of k for which the vectors v and w are perpendicular.v=3, k, -2 and w=-2, 1,…

Q: 18. Find the projection of (0,4) onto (3,7).

A: Answer

Q: Find the cross products u xv and vxu for the the vectors u = 2i-j-2k and v= i +3j - 3k. U XV= i+ j+k…

A: (.) Given vectors are,      (.) Corss product of two vectors  and   is given by,           &amp;…

Q: How did you get the vectors and to get a cross product for a perpendicular vector to i+j and j+k.

A: How did you get the vectors &lt;1,1,0&gt; and &lt;0,1,1&gt; to get a cross product for a…

Q: Find the angle between the two vectors u 2i+ j-7k and v =i-j+ 4k

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Q: Let V1 = 2 V2 = 0 2 V3 = 2 V4 = 3 Decide the dependence or independence of the vectors {V₁, V2, V₁}…

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