Two vectors ` vec A and vec B` are of equal lenths (A =B) and mutually perpendicualr. Show by vector diagram that their vector sum (vec A + vec B) and vetor differnce ( vec A - vec B) will perpendicular.

Explanation

Draw vec (PQ) = vec A` and from the arrow head of ` vec A`, draw vec (PS) = vec B`, of the same length ( i.e., QS =PQ) and perpendicular to ` vec A`. Fig. 2 (c ) 73. Now ` vec (PS)` will repesent ` (vec A + vec B) . Here,
` tan theta_(1) =(QS)/(PQ) =1 or ` theta _(1) =45^@
.
Now draw ` vec (QT) =- vec B`,
where ` QT =QD`. Now `vec (PT)` will represent
` (vec A- vec B)`. Here, ` tan theta_(2) =(QT)/(PQ) = 1 or theta_(2) = 45^@`
On measuring the lengths of (vec A = vec B) and (vec A - vec B) come out to be the same and angle between then, ` (theta_(1) + theta_2) = 45^@ + 45^@ = 45^@ =90^2`.