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  • The vector  is given as <img alt="\vec{A}=3\hat{i}+3\hat{j}" src="/latex-image/?%5Cvec%7BA%7D%3D3%5Chat%7Bi%7D&plus;3%5Chat

The vector \vec{A} is given as \vec{A}=3\hat{i}+3\hat{j}

Find the angle which the vector makes with the positive y-axis

Option: 1

\frac{\pi}{4}


Option: 2

\frac{\pi}{2}


Option: 3

\frac{\pi}{3}


Option: 4

\frac{\pi}{6}


Answers (1)

best_answer

Angle between \vec{A} and \hat{j} (unit vector along positive y-axis) is the angle between \vec{A} and positive y-axis

\\ cos\theta=\frac{A_xB_x+A_yB_y+A_zB_z}{(\sqrt{(A_x)^{2}+(A_y)^{2}+(A_z)^{2}}\sqrt{(B_x)^{2}+(B_y)^{2}+(B_z)^{2}}} \\ cos\theta=\frac{0+3+0}{\sqrt{(3)^{2}+(3)^{2}+(0)^{2}}}=\frac{3}{3\sqrt{2}}=\frac{1}{\sqrt{2}} \\ \theta=\frac{\pi}{4}

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manish painkra

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