Question

If magnitude of sum of two unit vectors is root 2 then find the magnitude of subtraction of these unit vector?

Answer 1

Answer:

$|\vec{a}-\vec{b}|=\sqrt3$

Explanation:

Let the two unit vectors be $\vec{a}\:and\:\vec{b}$

Then,

$|\vec{a}|=|\vec{b}|=1$

Given:

$|\vec{a}+\vec{b}|=\sqrt2$

We know that

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

$(1)^2+|\vec{a}-\vec{b}|^2=2((1)^2+(1)^2)$

$1+|\vec{a}-\vec{b}|^2=2(2)$

$|\vec{a}-\vec{b}|^2=4-1$

$|\vec{a}-\vec{b}|^2=3$

$|\vec{a}-\vec{b}|=\sqrt3$