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Angle between lines with direction ratios 2,3,-3 and 6,-3,1 will be

  • Option 1)

    \frac{\pi}{6}

  • Option 2)

    \frac{\pi}{4}

  • Option 3)

    \frac{\pi}{3}

  • Option 4)

    \frac{\pi}{2}

 

Answers (1)

best_answer

As we have learned

Ange between two lines in terms of direction cosines and direction ratios -

(i)    if two lines are parallel then

        l_{1}=l_{2}, m_{1}=m_{2}, n_{1}=n_{2} or

        \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}

(ii)     if two lines are perpendicular then

        l_{1}l_{2}+m_{1}m_{2}+n_{1}n_{2}= 0 or1

        a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}= 0

 

-

 

 here

a_{1}=2, b_{1}=3, c_{1}=-3

a_{2}=6, b_{2}=-3, c_{2}=1

 cos\theta =\frac {a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}

cos\theta= \frac{12-9-3}{\sqrt{12}\sqrt{46}}=0

\Rightarrow \theta=\frac{\pi}{2}

\therefore Option D


Option 1)

\frac{\pi}{6}

Option 2)

\frac{\pi}{4}

Option 3)

\frac{\pi}{3}

Option 4)

\frac{\pi}{2}

Posted by

Himanshu

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