For what value of `lambda` are the vectores ` 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 {i}+lambda {j}+{k}`


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


It is also given `vec{a} \ and\ vec{b}` are perpendicular.


Hence, their dot product is zero .


`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 `


`Rightarrow-2 lambda+5=0`


Hence, ` lambda \=\ frac{5}{2}`