Which one of the following is a two-point form equation for the line (x, y, z) = (1, 0, -1) + t(3,4, -1)? O A. (x, y, z) = (1, 0,2) + t(2, 1, -1) O B. (x, y, z) = (1 - 1)(2, 1, -1) + t(-1, -1,3) O C. (x, y, z) = (1 - 1)(1, 0,2) + t(2, 1, -1) O D. (x, y, z) = (1 - 1)(2, 1, -1) + t(1, 0,2) O E. (x, y, z) = (1 - t)(1, 0, -1) + 1(4, 4, -2)Find a vector parallel to the line 4x - 7y = 1. O A. (7,4) O B. (4, -7) O C. (4, 7) O D. (-7, 4) O E. (2, 1)Which one of the following is a point-normal form equation for the plane containing P(1, 2, 3) which is perpendicular to the vector u = (1, -2, -1)? O A. (1, -2, -1) . ((x, y, Z) - (1, 2,3)) = 0 O B. (1, 2, 3) . ((x, y, z) - (1, -2, -1)) = 0 O c. (1, 0, 1) . ((x, y, z) - (1, 2,3)) = 0 O D. (1, 2, 3) . (x, y, z) = (1, 2,3) . (1, -2, -1) O E. (1, 1, -1) . ((x, y, z) - (1, -2, -1)) = 0\f\fFind the value of k for which the vectors D = (2, 6, -2, 2) and w = (1,3, -1, k) are orthogonal. O A. -2 O B. -11 O c. 1 O D. 2 O E. 11Consider line & containing points (1, 1, 1, 1) and O(1, 0, 4, 3). Let u = (u1, u2, u3, u4 ) be a direction vector for line . Which of the following statements always must be true? 1. u1 = 0 2. u2 = -1 3. u4 = -2u2 O A. none of them O B. 1. and 3. only O C. 1. only O D. 2. and 3. only O E. all of themWhich one of the following points lies on the hyperplane in R with standard form equation x1 - x3 + 3x5 = -6? A. (3, 3, 0, 0, 0) O B. (-1, 0, 2, 1, 1) O C. (1, 0, 7, 0, 1) O D. (-2, 0, -8, -1,0) O E. (2, 0, 14, 12, 2)