The line through the points A(2, −1, 1) and B(4, 3, k) is perpendicular to the line \(\displaystyle\frac{x-1}{1}=\frac{y+2}{1}=\frac{z}{2}\). The value of k is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → −2
The direction ratios of the line AB are the differences of the coordinates of B and A:
\(4-2 = 2,\quad 3-(-1) = 4,\quad k-1\)
The given line has direction ratios 1, 1, 2. Two lines are perpendicular when \(a_1a_2+b_1b_2+c_1c_2 = 0\):
\((2)(1)+(4)(1)+(k-1)(2) = 0\)
\(2k+4 = 0\)
\(k = -2\)