Question

Determine the value of a, so that If α=2i+aj+k and \eta=4i−j−2k are perpendicular.

a.2
b.5
c.4
d.3

Answer 1

Vectors $\alpha=(2,a,1)$ and $\beta = (4,-1,-2)$ are perpendicular if and only if their dot product is equal to zero.

$$(2,a,1)\cdot(4,-1,-2)=0$$ $$2\cdot 4+a\cdot(-1)+1\cdot(-2)=0$$ $$8-a-2=0$$ $$6-a=0$$ $$a=6$$

Answer: 6