Question

If A, B, C, D are the points (3, 4, 5) (4, 6, 3), (–1, 2, 4) and

(1, 0, 5), then the projection of CD on AB is

• A. $\frac { 3 } { 4 }$
• B. $\frac { - 4 } { 3 }$
• C. $\frac { 3 } { 5 }$
• D. None of these

Answer 1

Answer: (B)

$\frac { - 4 } { 3 }$

Answer 2

Let l, m, n be the direction cosines of AB

Then $l = \frac { 4 - 3 } { \sqrt { ( 4 - 3 ) ^ { 2 } + ( 6 - 4 ) ^ { 2 } + ( 3 - 5 ) ^ { 2 } } } = \frac { 1 } { 3 }$ , $m = \frac { 6 - 4 } { 3 } = \frac { 2 } { 3 }$.

Similarly $n = \frac { - 2 } { 3 }$

∴ The projection of CD on AB