Question

A vector of components (6, 2) is multiplied by the scalar value of 3. What is the magnitude and direction of the resultant vector?

Answer 1

Answer:

18.97∡18.43

Explanation:

To find the magnitude of this vector we have to use the Pythagorean theorem, since we have the magnitudes on the X & y axes.

x = 6

y = 2

$d=\sqrt{x^{2} +y^{2} }\\d = \sqrt{6^{2} +2^{2} }\\d = 6.32$

After multiplying the magnitude by 3 we have:

D = 6.32*3

D = 18.97

The direction of the vector doesn't change only the magnitude

tan(α) = 2/6

α = tan⁻¹(2/6)

α = 18.43°

So the first vector is equal to: 6.32∡18.43

and the second vector is: 18.97∡18.43