The angle between vector A = 2.00i + 3.00j and vector B is 45.0°. The scalar product of vectors A 12) and B is 7.00. If the x-component of vector B is positive, what is vector B

B = 2.67i - 0.53j

Explanation:

In order to find the vector B, you first take into account the following formula:

        (1)

where:

A = 2.00i + 3.00j

B = ?

θ: angle between vectors A and B = 45.0°

You use the fact that the dot product between vectors A and B is 7.00.

You calculate the magnitude of A vector as follow:

Then, you solve the equation (1) for the magnitude of B:

Next, you can consider that the A vector is the x axis of the coordinate system, to calculate the components of B. This means that the coordinate system is rotated an angle equivalent to the angle of A respect to the x axis.

With the previous assumption you have that the components of B are:

The vector B is:

B = 1.93i + 1.93j

Next, it is necessary to rotate again the coordinate system to its original position. For that, you calculate the angle of A:

In order to calculate the real components of B, you rotate the system 56.30°, by using the following relation:

The vector B is:

B = 2.67i - 0.53j

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