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  • Solve this problem - Three dimensional Coordinate Geometry - BITSAT

Two lines whose direction rations are:<a_1, b_1, c_1 > \:and \: <a_2,b_2,c_2 >respectively are perpendicular if

  • Option 1)

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

  • Option 2)

    \frac{a_1}{b_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}

  • Option 3)

    a_1a_2 + b_1b_2 +c_1c_2=0

  • Option 4)

    a_1a_2+b_1b_2+c_1c_2 =1

 

Answers (1)

best_answer

 

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 or

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

 

-

 

 


Option 1)

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

Incorrect

Option 2)

\frac{a_1}{b_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}

Incorrect

Option 3)

a_1a_2 + b_1b_2 +c_1c_2=0

Correct

Option 4)

a_1a_2+b_1b_2+c_1c_2 =1

Incorrect

Posted by

Aadil

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