Physics - Vectors Question with Solution | TestHub

Since the vectors $\vec{P}$ and $\vec{Q}$ are perpendicular to each other, their dot product is zero.

$\vec{P}\cdot \vec{Q}=0$

$(b\hat{i}+6\hat{j}+\hat{k})\cdot (\hat{i}-a\hat{j}+4\hat{k})=0$

$b(1)+6(-a)+1(4)=0$

$b-6a+4=0$

It is given that $3b-a=5$, which gives $a=3b-5$.

Substituting the value of $a$ in the dot product equation:

$b-6(3b-5)+4=0$

$b-18b+30+4=0$

$-17b+34=0$

$17b=34$

$b=2$

Substituting $b=2$ in $a=3b-5$:

$a=3(2)-5=1$

Thus, $a=1$ and $b=2$.

Answer: $a=1,b=2$