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Question: If A (1, 2, 3), B(6, 7, 8) C(1,2, 5) and D (3, 0, 4) are given points, then the projection of \(\ov...

If A (1, 2, 3), B(6, 7, 8) C(1,2, 5) and D (3, 0, 4) are given points, then the projection of AB↔\overleftrightarrow { \mathrm { AB } } on CD↔\overleftrightarrow { \mathrm { CD } } is

A

1/3

B

4/3

C

25/3

D

5/3

Answer

5/3

Explanation

Solution

Sol. D.R's of are (2, -2, -1) or (-2, 2, 1)

∴\therefore**D.C'**s of are (−23,23,13)\left( \frac { - 2 } { 3 } , \frac { 2 } { 3 } , \frac { 1 } { 3 } \right)

Projection of AB‾\overline { \mathrm { AB } }on

CD = (6−1)(−23)+(7−2)(23)+(8−3)(13)( 6 - 1 ) \left( - \frac { 2 } { 3 } \right) + ( 7 - 2 ) \left( \frac { 2 } { 3 } \right) + ( 8 - 3 ) \left( \frac { 1 } { 3 } \right)

= 5(−2+2+13)=535 \left( \frac { - 2 + 2 + 1 } { 3 } \right) = \frac { 5 } { 3 }