Question

Find $\arrowvert\vec x\arrowvert$, if for a unit vector $\vec a, (\vec x - \vec a).(\vec x + \vec a)=12$.

Answer 1

Answer:

$|\vec{x}|=\sqrt{13}$

Step-by-step explanation:

Formula used:

$(\vec{a}+\vec{b}).(\vec{a}-\vec{b})=|\vec{a}|^2-|\vec{b}|^2$

$Given:\\\\\vec{a}\:is\:a\:unit\:vector\\\\Then,\\\\|\vec{a}|=1\\\\Also,\\\\(\vec{x}+\vec{a}).(\vec{x}-\vec{a})=12\\\\|\vec{x}|^2-|\vec{a}|^2=12\\\\|\vec{x}|^2-(1)^2=12\\\\|\vec{x}|^2=12+1\\\\|\vec{x}|^2=13\\\\|\vec{x}|=\sqrt{13}$