Question

A line \(L_1\) passing through the point \(A\) with position vector \( \vec{a} = 4\hat{i} + 2\hat{j} + 2\hat{k} \) is parallel to the vector \( \vec{b} = 2\hat{i} + 3\hat{j} + 6\hat{k} \). The length of the perpendicular drawn from a point \(P\) with position vector \( \vec{p} = \hat{i} + 2\hat{j} + 3\hat{k} \) to \(L_1\) is

• A. 0
• B. \( \sqrt{15} \)
• C. \( 2\sqrt{3} \)
• D. \( \sqrt{10} \)

Hint:

Distance from a point to a line in vector form is given by \( \frac{|\vec{AP} \times \vec{d}|}{|\vec{d}|} \), where \( \vec{d} \) is the direction vector.

Answer 1

The Correct Option is D