Question

Vector A has a magnitude of 30 units. Vector B is perpendicular to vector Aand has a magnitude of 40 units. What would the magnitude of the resultant vector A + B be?

Answer 1

`|\vec A + \vec B| = 50 units`

Step-by-step explanation:

As we know that magnitude of two vectors is given as

`|\vec A + \vec B| = √(A^2 + B^2 + 2AB cos\theta)`

here we know that

A = magnitude of vector A

B = magnitude of vector B

`\theta` = angle between two vectors

so here we know that

A = 30 units

B = 40 units

angle = 90 degree

so we have

`|\vec A + \vec B| = √(30^2 + 40^2 + 2(30)(40)cos90)`

`|\vec A + \vec B| = √(30^2 + 40^2)`

`|\vec A + \vec B| = 50 units`