91影视

Vector is easily defined with the help of their magnitude and their angle with the x and the y-axes.

Here, in this case, there are four vectors given

For this vector, we will take the use of magnitude given as well as the angle with the x-axis and the y-axis.

For the direction shown in the graph as:

As here, the vector is precisely on the y-axis, so the magnitude with respect to the y-axis will be zero.

The angle of that vector made with the x-axis will be 90 鈥� 30 = 60.

Hence the components of the b vector will be magnitude multiplied by the cos angle and sin angle made with respect to the x-axis as:

$$\begin{gathered} \stackrel{鈫�}{B}=15\cos 鈦�{60}^{鈭�}\widehat{i}+15\sin 鈦�{60}^{鈭�}\widehat{j} \\ =7.5\widehat{i}+13\widehat{j} \\ \stackrel{鈫�}{B}=(7.5,13)\mathrm{m} \end{gathered}$$

$$\begin{gathered} \stackrel{鈫�}{C}=鈭�12\cos 鈦�{25}^{鈭�}\widehat{i}鈭�12\sin 鈦�{25}^{鈭�}\widehat{j} \\ =鈭�10.87\widehat{i}鈭�5.07\widehat{j} \\ =(鈭�10.87,鈭�5.07)\mathrm{m} \end{gathered}$$

$$\begin{gathered} \stackrel{鈫�}{D}=10\cos 鈦�{53}^{鈭�}\widehat{j}鈭�10\sin 鈦�{53}^{鈭�}\widehat{i} \\ =6.018\widehat{j}鈭�7.986\widehat{i} \\ =(鈭�7.986,6.018)\mathrm{m} \end{gathered}$$

Hence, the x and the y components of vectors A, B, C and D are (0, 鈥�8), (7.5,13), (鈥�10.88, 鈥�5.07) and (鈥�7.99, 6.02), respectively.