Maharashtra State BoardHSC Arts 12th Board Exam
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If the line r=(i-2j+3k)+λ(2i+j+3k) is parallel to the plane r.(3i-2j+pk)=10 find the value of p. - Mathematics and Statistics

`barr=(hati-2hatj+3hatk)+lambda(2hati+hatj+2hatk)` is parallel to the plane `barr.(3hati-2hatj+phatk)=10`, find the value of p.

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Solution

`barb=2hati+hatj+2hatk`

`hatn=3hati-2hatj+phatk`

Since, line is parallel to the plane

`bar b.hatn=0`

`(2hati+hatj+2hatk).(3hati-2hatj+phatk)=0`

`(6-2+2p)=0`

`p=-2`

Concept: Plane - Equation of Plane Passing Through the Given Point and Parallel to Two Given Vectors
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