# 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.

#### 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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