Determine if the following statement is true or false.

l. (2 points) Determine if the following statement is true or false. If the statement is false, correct it by determining what the right hand side of the equation should be. Briey explain your answer. NO credit will be given for a one-word answer. ()x(+)=xfix 2. (2 points) Verify the following M11. + 13) = k If + k I? for any scalar k and vectors If and 13 in IR\". 4. (10 points) Let a = (3, 5,1), 13 = (2,0,2), and E" = (0, 1,4). Compute the following. Ifa computation is not possible, briey explain why. .LFz'l F-'Ll. Fill Fill E-(-W) H317\" +||-213|| + \"I3 + W\" Projw' D'UGFHCDg-Oc'm F: x . ("N d X El \\._/ Component of H orthogonal to W . . I I j. LetA = 2 1 3 3 2 4 1 2],=[5] and=[ U ]. FindA-13andverifythatitgivesthesame 1 3 1 1 2 result as a - Arr-5. 5. (2 points) Find all values of a (if any) so that the vectors 3 = (1,0,2), 13 = (4,3,2), and w = (6, a, 3) form an orthogonal set. 6. (4 points) Find the following a. The vector equation of the plane containing the point (1, 4,4) and the vectors 13 = (0,5, 2) and 11' = (4, 1,5). b. The parametric equations of the line in R2 that passes through the point (4, 2) and is orthogonal to i5 = (3, 2) c. The vector equation of a line in R3 containing the point (8,1, 3) and parallel to the vector 13 = (4, 2, 5)