Question

If the magnitude of sum of two non zero vectors is equal to the magnitude of their difference, then which of the following is true?

.Two vectors must have equal magnitude

.Angle between two vectors must be 90°

.Two vectors have equal magnitude but oppositely directed

.Angle between the vectors must be, 120°​

Answer 1

Given:

Magnitude of sum of two non-zero vectors= the magnitude of their difference  i.e. |a→ + b→| = |a→ - b→|

To find:

Which of the given options are correct.

Solution:

Since the magnitude of the sum of two non-zero vectors is equal to the magnitude of their difference.

Let the vectors be a→ and b→.

|a→ + b→| = |a→ - b→|

a²+b² - 2abcosα = a²+b² + 2ab cosα

4ab cosα = 0

cos α = 0

α = 90°

Since the vectors are perpendicular, the correct option is b.

The angle between two vectors must be 90° is the correct option.