Question

Determine the value of 𝑎 so that 𝑨 = 2𝒊 − 𝑎𝒋 + 𝒌 and 𝑩 = 4𝒊 − 2𝒋 − 2𝒌 are perpendicular.

Answer 1

$A=(2,-a,1)$, $B=(4,-2,-2)$.

Two vectors are perpendicular iff $A\cdot B=0$.

$A\cdot B=2\cdot4 + (-a)\cdot(-2) + 1\cdot(-2)=8+4a-2=4a+6$.

$4a+6=0$, so $a=-\frac32$.