Write the value of `lambda` so that 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` are 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}`


For finding perpendicular,


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


`Rightarrow 2 times 1+lambda(-2)+1 times 3=0`


`Rightarrow 2 lambda=5`


`Rightarrow lambda=frac{5}{2}`