For what value of `lambda` asre the vector ` vec a=2 hat i+lambda hat j+ hat k\ a n d\ vec b= hat i-2 hat j+3 hat k` perpendicular to each other?

Explanation

Given: `vec{a}=2 hat{i}+lambda hat{j}+hat{k}`


Given: ` vec{b}=hat{i}-2 hat{j}+3 hat{k}`


Given:` vec{a} and vec{b}` are perpendicular.


`Rightarrow vec{a} cdot vec{b}=0`


`Rightarrow(2 hat{i}+lambda hat{j}+hat{k}) cdot(hat{i}-2 hat{j}+3 hat{k})=0 `


`Rightarrow 2-2 lambda+3=0`


So,


`5-2 lambda=0`


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