Question

The image of point (1, 2, 3) in the line

$r = ( 6 i + 7 j + 7 k ) + \lambda ( 3 i + 2 j - 2 k )$ is

• A. (5, –8, 15)
• B. (5, 8, –15)
• C. (–5, –8, –15)
• D. (5, 8, 15)

Answer 1

Answer: (D)

(5, 8, 15)

Answer 2

Given that, , $b = 3 i + 2 j - 2 k$ and

Then, $\vec { \beta } = 2 a - \left( \frac { 2 ( a - \vec { \alpha } ) \cdot b } { | b | ^ { 2 } } \right) b - \vec { \alpha }$

On solving, .

Thus $\vec { \beta }$is the position vector of Q, which is the image of P in given line.

Hence image of point (1, 2, 3) in the given line is (5, 8, 15)