Find the orthogonal decomposition of v with respect to W. 1 --[-]-~-~~-~(:][-D) -2 W = span 2 1 V projw(v) = perpw(v) = 4 3 000 000 1 -1 1

the vertices A(-2,-1), B(-3,2), C(-1,3), and D(0,0) form a prallelogram. The vertices A'(-1,-2), B'(2,-3), C'(3,-1) and D's(0,0) are the image of the parallelogram after a sequence of transformations. which sequence of transformations could produce the image from the pre-image?

Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by the vectors (-3,7) and (9,3). (Use symbolic notation and fractions where needed. Give your answer in the form (*, *).) G(u, v) =

Find the scalar equation of the line through (3,-2) and perpendicular to the line r = (4,-3) + t(-5,1) .  Please answer.  Thank you

Compute the orthogonal projection of i = -5 onto the line L through 2 and the origin.

Let Ly be the line passing through the point P-(10, 1, -10) with direction vector d-[-2, -2, 3]", and let L2 be the line passing through the point P-(-10, 21, -6) with direction vector d,-[-2, -6, -1]". Find the shortest distance d between these two lines, and find a point Q, on L, and a point Q, on L2 so that d(Q7 Q2) = d. Use the square root symbol W where needed to give an exact value for your answer. d = 0 Qi = 1%3D(0,0,0) Q2 = (0, 0, 0)

If vector A = [4,1] and vector B = [-3,2] and A-B = [-1,-1]  Sketch the computation above and represent it as a vector addition

Let a = (-4, 3, 4) and b = (-5, 2, 3), then find the decomposition a = a +a of a with respect to b a = | help (vectors) aj =

Find the 2. equation of the place that Pusses +2 through the point= (-1,2,1) 3 Contains the line of intersection of the places Vty -7-2 3 zxay +3z=| (12)23,20271115) Xy2z-9 -121212/0 02/02 Paile 2,350

In parallelogram WXYZ, diagonals WY and XZ intersect at point A. Give WA = x^2 - 48 and AY = x^2 - 6x. What is WY? Show your work