If the vectors `3 hat i+lambda hat j+ hat k\ a n d\ 2 hat i- hat j+8 hat k` are perpendicular, then `lambda` is equal to a.`-14` b. `7` c. `14` d. `1/7`

Explanation

We have,

`vec{a}=3 vec{i}+lambda vec{j}+vec{k} `

`vec{b}=2 vec{i}-vec{j}+8 vec{k}`

Given that `vec{a} and vec{b} ` are perpendicular

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

`Rightarrow(3 vec{i}+lambda vec{j}+vec{k}) cdot(2 vec{i}-vec{j}+8 vec{k})=0 `

`Rightarrow 6 cdot lambda+8=0 `

`therefore lambda=14`

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