Question

The x and y-components of vector A are 4 m and 6 m respectively. The x and y-components of vector A + B are 10 m and 9 m respectively. Calculate for the vector B the following: (a) its x and y-components (b) its length (c ) the angle it makes with x-axis.

Answer 1

The vector B, its components, its length and the angle made by it with the x-axis is:

• Given, A's x-component = 4 m

        A's y-component = 6 m

        Hence, A = (4 i + 6 j) m

• Given, (A+B)'s x-component = 10 m

        (A+B)'s y-component = 9 m

        Hence, A+B = (10 i + 9 j) m

• B= (A+B)-A = (6 i + 3 j) m

• Therefore, B's x-component = 6 m

        B's y-component = 3 m

• Length of B = $\sqrt{6^2+3^2} =\sqrt{45} = 3\sqrt{5} m$

• Angle it makes with the x-axis = Θ

        tan Θ = $\frac{3}{6}$  ⇒  Θ = $tan^{-1} (0.5)$