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  • If the foot of the perpendicular drawn from the point (1,0,3) on line passing through  is 

If the foot of the perpendicular drawn from the point (1,0,3) on line passing through (\alpha ,7,1) is \left ( \frac{5}{3},\frac{7}{3},\frac{17}{3} \right ), then \alphais equal to _______.
Option: 1 2
Option: 2 4
Option: 3 8
Option: 4 10
 

Answers (1)

best_answer

 

 

Angle Between Two Lines -

Vector Form
Condition for Perpendicularity

The lines are perpendicular then cos? = 90o

\\\teaxt{i.e.}\mathrm{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\vec{\mathbf b}\cdot\vec{\mathbf b}'=0\;\;\;\;\;\;\;\;\;\;\;\;\; \left [\because\;\; \cos90^\circ=0 \right ]\\\\\Rightarrow\;\;\;\;a_1a_2+b_1b_2+c_1c_2=0


Condition for parallelism

The lines are parallel then \vec{\mathbf b}=\lambda\vec{\mathbf b}' for some scalar λ.

\Rightarrow \;\;\;\;\;\;\;\;\;\;\;\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}

-

Since PQ is perpendicular to L, therefore

\\\left ( 1-\frac{5}{3} \right )\left ( \alpha-\frac{5}{3} \right )+\left ( -\frac{7}{3} \right )\left ( 7-\frac{7}{3} \right )+\left ( 3-\frac{17}{3} \right )\left ( 1-\frac{17}{3} \right )=0\\\alpha=4

Posted by

Ritika Jonwal

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