Question

The straight line \( r = (i - j + k) + \lambda (2i + j - k) \) and the plane \( r \cdot (2i + j - k) = 4 \) are

• A. Perpendicular to each other
• B. Parallel
• C. Inclined at an angle 60°
• D. Inclined at an angle 45°

Answer 1

The Correct Option is A

Direction vector of line = \( \vec{d} = \langle 2, 1, -1 \rangle \) Normal vector of plane = \( \vec{n} = \langle 2, 1, -1 \rangle \) If dot product = 0 → perpendicular. \[ \vec{d} \cdot \vec{n} = 2 \cdot 2 + 1 \cdot 1 + (-1)\cdot(-1) = 4 + 1 + 1 = 6 \neq 0 \] Wait! But direction vector of line is same as normal to plane ⇒ they are perpendicular.