Question

Two vectors inclined at an angle have magnitude 3N and 5N and their resultant is of magnitude 4N.The angle dete is

Answer 1

3,4,5 describes the ratio of the lengths of a particular right triangle. So the angle between the 3 and the 4 is 90 degrees.

Answer 2

Answer:

The angle between the vectors is 53°.

Explanation:

The resultant of vectors inclined at an angle is given as,

$R=\sqrt{A^{2}+B^{2}+2ABcos\theta }$       (1)

Where,

R=resultant of the vectors

A=magnitude of the first vector

B=magnitude of the second vector

cosθ=angle between the vectors

As per the question we have,

A=3N

B=5N

R=4N

By substituting the required values in equation (1) we get;

$4=\sqrt{3^{2}+5^{2}+2\times 3\times 5\times cos\theta }$

$16=34+30cos\theta$

$18=30cos\theta$

$cos\theta=\frac{18}{30}=\frac{3}{5}$

$\theta=53\textdegree$

Hence, the angle between the vectors is 53°.