Question

13) Can two nonzero perpendicular vectors be added together so their sum is zero? Explain.

Answer 1

Answer:

sum of two perpendicular nonzero vectors can not be ZERO

Explanation:

As we know by the sum or addition of two vectors is given by

$R = \sqrt{a^2 + b^2 + 2abcos\theta}$

here we know that

a and b are the magnitude of two vectors

$\theta$ = angle between two vectors

so as we know that here two vectors are perpendicular to each other

so we will have

$R = \sqrt{a^2 + b^2}$

now since the is sum of two positive non zero numbers so it can not be zero

so sum of two perpendicular nonzero vectors can not be ZERO

Answer 2

In order for two vectors to add to zero, they must have the same magnitude and point in opposite directions.

Two perpendicular vectors, by definition, make a right angle with each other whereas two vectors pointing in opposite directions form a straight line.

Because of this, two perpendicular vectors with nonzero magnitudes will never add to zero.