Question

Two vectors, X and Y, form a right angle. Vector X is 48 inches long and vector Y is 14 inches long. The length of the resultant vector is inches.

Answer 1

Z=X+Y(Z,Y,X-vectors); Z=√(X^2+Y^2)=50 inches

Answer 2

As per the question length of X =48 inches

The length of Y=14 inches.

Both X and Y are vectors.

We are asked to calculate the length of resultant vectors.

The two vectors are perpendicular to each other.Hence, the angle between them is 90 degree.

As per parallelogram law of vector addition,the magnitude of resultant vector is given as-

`R =\sqrt{X^(2)+ Y^(2) +2XY\cos\theta}\ \ \ where\ \theta\ is\ the\ angle\ between\ them`

Here R stands for magnitude of X and Y.

`=\sqrt{ [48]^(2)+[14]^(2) +2*48*14*cos90}`

`=√(2304+196+0)` [cos90=0]

`=√(2500)`

`=50 inches` [ans]