Question

i and j are unit vectors along x- and y-axis respectively. What is the magnitude and direction of the vectors i + j and i− j ? What are the components of a vector A = 2i and 3j along the directions of i + j and i – j ? [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 i + j is √2 .

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

Hence, the magnitude of the vector i − j is √2.

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

On comparing the coefficients of i and j, we have:

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

..............(v)

Component of vector , along the direction of , making and angle θ.