Find the value of `lambda` for which the planes.
`vecr.(hati+2hatj+3hatk)=13` and `vecr.(lambdahati+2hatj-7hatk)=9`, are perpendicular to each other.

Explanation

We know that the planes `vecr.vecn_(1)=q_(1)` and `vecr.vecn_(2)=q_(2)` are perpendicular to the each other only when `vecrn_(1).vecn_(2)=0`.
Here, `vecn_(1)=(hati+2hatj+3hatk)` and `vecn_(2)=(lambdahati+2hatj-7hatk)`.
`therefore` the given planes are perpendicular to the each other.
`ltimplies vecn_(1).vecn-(2)=0`
`ltimplies (hati+2hatj+3hatk).(lambdahati+2hatj-7hatk)=0`
`ltimplies 1 xx lambda + 2 xx 2+3 xx (-7) =0 ltimplies lambda=17`.
Hence, the required value of `lambda` is 17.