Find the value of `lambdadot` If the vectors `2 hat i+lambda hat j+3 hat k\ a n d\ 3 hat i+2 hat j-4 hat k` are perpendicular to each other.

Explanation

It is given that, 2 hat{i}+lambda hat{j}+3 hat{k} and 3 i+2 j-4 k are perpendicular to each other.


Hence, their dot product is zero.


`(2 hat{i}+lambda hat{j}+3 hat{k}) cdot(3 i+2 j-4 k) `


`Rightarrow 6+2 lambda-12=0 `


`Rightarrow 2 lambda-6=0 `


`Rightarrow lambda=3`