**Q.No.2.12: - Show that the sum and difference of two perpendicular vectors of equal lengths are also perpendicular and of the same length.**

**Ans: -**Let us suppose there are two vectors A and B which are equal in magnitude and perpendicular to each other.

According to head to tail rule,

Hence we can say that

**R**is perpendicular to Ro. Therefore, both sum and difference are perpendicular to one another. Now by using the formula for magnitude of rectangular components, we have
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