Let A be a point on the line [ r = ( 1 - 3 ) i + ( - 1 ) j + ( 2 + 5 ) k] and B(3, 2, 6) b…

Question

Let A be a point on the line $$\overrightarrow r  = \left( {1 - 3\mu } \right)\widehat i + \left( {\mu  - 1} \right)\widehat j + \left( {2 + 5\mu } \right)\widehat k$$ and B(3, 2, 6)  be a point in the space. Then the value of $$\mu $$ for which the vector $$\overrightarrow {AB} $$  is parallel to the plane x - 4y + 3z = 1 is -

Accepted Answer

Let point A is

$$\left( {1 - 3\mu } \right)\widehat i + \left( {\mu  - 1} \right)\widehat j + \left( {2 + 5\mu } \right)\widehat k$$

and point B is (3, 2, 6)

then $$\overrightarrow {AB}  = \left( {2 + 3\mu } \right)\widehat i + \left( {3 - \mu } \right)\widehat j + \left( {4 - 5\mu } \right)\widehat k$$

which is parallel to the the plane x - 4y + 3z = 1

$$ \therefore $$  2 + 3$$\mu $$ - 12 + 4$$\mu $$ + 12 - 15$$\mu $$ = 0

8$$\mu $$ = 2

$$\mu $$ = $${1 \over 4}$$

Solutions · 1