Question

(xiv) If the magnitude
magnitude of sum of two vectors is
equal to the magnitude of difference of two
vectors, the angle between these vectors is
(a) o°(b) 10° (6 45° (d) 180°​

Answer 1

Answer:

sum of two vectors

= √a^2+ b^2+2ab×cos theta

difference of two vectors

= √a^2+ b^2-2ab× cos theta

according to the question,

√a^2 + b^2 + 2ab×cos theta

=√a^2 + b^2 - 2ab×cos theta

squaring on both sides,

a^2 + b^2 + 2ab×cos theta

= a^2 + b^2 - 2ab×cos theta

that is,

4ab×cos theta = 0

4ab depends on a and b and can never be 0

so, here, cos theta should be 0

cos theta = 0

theta = 90°