The projection of the line segment joining P(2,-1,0) and Q(3,2,-1) on the line whose direction ratios are 1,2,2 is

Step-by-step solution

The projection of the vector PQ onto a line with direction cosines (l, m, n) is given by the absolute value of A_x l + A_y m + A_z n . First, compute PQ = (3-2, 2-(-1), -1-0) = (1, 3, -1) . Given direction ratios (1,2,2) , the magnitude is 1^2 + 2^2 + 2^2 = 3 . Thus, the direction cosines are ( 1 3 , 2 3 , 2 3 ) . The projection evaluates to |1 1 3 + 3 2 3 + (-1) 2 3 | = | 1 3 + 6 3 - 2 3 | = 5 3 . The final answer is D .