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 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= 2   i j + 3 along the directions of   i j + and   i j − ? [You may use graphical method]

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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...
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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

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