Question

The equation of the line through the point (0, 1, 2) and perpendicular to the line (x-1)/2 = (y+1)/3 = (z-1)/(-2) is:

• A. x/3 = (y-1)/4 = (z-2)/(-3)
• B. x/(-3) = (y-1)/4 = (z-2)/3
• C. x/3 = (y-1)/(-4) = (z-2)/3
• D. x/3 = (y-1)/4 = (z-2)/3

Hint:

If a line is perpendicular to another, the dot product of their direction ratios must be zero: $a_1a_2 + b_1b_2 + c_1c_2 = 0$.

Answer 1

The Correct Option is B

Step 1: Let DRs of the required line be $(a, b, c)$. Since it is perpendicular to $(2, 3, -2)$, $2a + 3b - 2c = 0$.
Step 2: Check options for dot product with $(2, 3, -2) = 0$.
Step 3: For (B): $2(-3) + 3(4) - 2(3) = -6 + 12 - 6 = 0$. This is the only valid direction.