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  • If are such that is perpendicular to , then find the value of .

Q10   If  \vec a = 2 \hat i + 2 \hat j + 3 \hat k , \vec b = - \hat i + 2 \hat j + \hat k \: \: and \: \: \vec c = 3 \hat i + \hat j are such that \vec a + \lambda \vec b is perpendicular to \vec c  , then find the value of \lambda

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best_answer

Given in the question is

\vec a = 2 \hat i + 2 \hat j + 3 \hat k , \vec b = - \hat i + 2 \hat j + \hat k \: \: and \: \: \vec c = 3 \hat i + \hat j

and  \vec a + \lambda \vec b is perpendicular to \vec c 

 and we need to find the value of \lambda,

so the value of \vec a + \lambda \vec b-

\vec a + \lambda \vec b=2\hat i +2\hat j +3\hat k+\lambda (-\hat i+2\hat j+\hat k)

\vec a + \lambda \vec b=(2-\lambda)\hat i +(2+2\lambda)\hat j +(3+\lambda)\hat k

As  \vec a + \lambda \vec b is perpendicular to \vec c

(\vec a + \lambda \vec b).\vec c=0

((2-\lambda)\hat i +(2+2\lambda)\hat j +(3+\lambda)\hat k)(3\hat i+\hat j)=0

3(2-\lambda)+2+2\lambda=0

6-3\lambda+2+2\lambda=0

\lambda=8

the value of \lambda=8,

Posted by

Pankaj Sanodiya

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