Write the value of `lambda` for which the lines `(x-3)/(-3)=(y+2)/(2lambda)=(z+4)/2a n d(x+1)/(3lambda)=(y-2)/1=(z+6)/(-5)` are perpendicular to each other.

Explanation

As we have given

`(x-3)/(-3)=(y+2)/(2lambda)=(z+4)/2a n d(x+1)/(3lambda)=(y-2)/1=(z+6)/(-5)`

Then

`vec(b_1)=-3hat(i)+2lambda hat(j)+2hat(k)` and `vec(b_2)=3lambda hat(i)+hat(j)-5hat(k)`

As the given lines are perpendicular to each other

`implies vec(b_1).vec(b_2)=0`

`implies (-3hat(i)+2lambda hat(j)+2 hat(k)).(3lambda hat(i)+hat(j)-5hat(k))=0`

`implies -7lambda -10=0`

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