Question

are unit vectors along x- and y-axis respectively. What is the magnitude and direction of the vectorsand? What are the components of a vectoralong the directions of and? [You may use graphical method]

Answer 1

Consider a vector, given as:

On comparing the components on both sides, we get:

Hence, the magnitude of the vector is .

Let be the angle made by the vector, with the x-axis, as shown in the following figure.

Hence, the magnitude of the vector is .

Let be the angle made by the vector, with the x- axis, as shown in the following figure.

It is given that:

On comparing the coefficients of , we have:

Let make an angle with the x-axis, as shown in the following figure.

Angle between the vectors

Component of vector , along the direction of , making an angle

Let be the angle between the vectors.

Component of vector, along the direction of, making an angle