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Question

Equation of plane passing through points given by position vectors ¯a and ¯b and origin will be


A

¯r.¯a¯b|¯aׯb|=0.

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B

¯r.¯a+¯b|¯aׯb|=0.

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C

¯r.¯aׯb|¯aׯb|=0.

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D

¯r.(¯a.¯b|¯aׯb|)=0.

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Solution

The correct option is C

¯r.¯aׯb|¯aׯb|=0.


Here we know given the plane passes through points given by position vectors ¯a and ¯b . So the perpendicular to the plane will be along ¯aׯb. Therefore our ^n or unit vector perpendicular to the plane will be ¯aׯb|¯aׯb|. Equation of plane will be

(¯r0).¯aׯb|¯aׯb|=0.

Which is same as,

¯r.¯aׯb|¯aׯb|=0.


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