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Vector b~ has x, y, and z components of 4.4, 9.6, and 5 units, respectively. what is the angle between b~ and the x-axis?

User Omtechguy
by
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1 Answer

5 votes
The simplest vector you can take along the x-axis is
\mathbf v=langle1,0,0\rangle.

Now,


\mathbf b\cdot\mathbf v=\|\mathbf b\|\|\mathbf v\|\cos\theta

where
\theta is the angle between the two vectors. You have


\mathbf b\cdot\mathbf v=\langle4.4,9.6,5\rangle\cdot\langle1,0,0\rangle=4.4

\|\mathbf b\|=√(4.4^2+9.6^2+5^2)\approx11.68

\|\mathbf v\|=√(1^2+0^2+0^2)=1

so that


4.4=11.68\cos\theta\implies\cos\theta=0.3767\implies \theta\approx67.87^\circ
User Salvin
by
8.1k points

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