The vector that must be added to i -3 j +2 k and 3 i +6 j -7 k so resultant vector is a unit vector along the X - axis is

Step-by-step solution

Let the given vectors be A = i - 3 j + 2 k and B = 3 i + 6 j - 7 k . Let the vector to be added be V = x i + y j + z k . The resultant vector is a unit vector along the X-axis, which is i . Therefore, A + B + V = i . ( i - 3 j + 2 k ) + (3 i + 6 j - 7 k ) + (x i + y j + z k ) = i . (1 + 3 + x) i + (-3 + 6 + y) j + (2 - 7 + z) k = i . (4 + x) i + (3 + y) j + (-5 + z) k = 1 i + 0 j + 0 k . Equating the components: 4 + x = 1 x = -3 3 + y = 0 y = -3 -5 + z = 0 z = 5 Thus, V = -3 i - 3 j + 5 k . Answer: -3 i -3 j +5 k