The direction angle and magnitude of the position vector are 34 degrees and 7.93 respectively.
Direction of a vector:
The direction of a vector is the orientation of the vector, that is the angle it makes with the x- axis.
Formula for finding the magnitude of the vector:
If position vector v = <a, b>, then the magnitude is given by
[tex]|v| = \sqrt{a^{2}+b^{2} }[/tex]
Formula for finding the direction of a vector
If θ is the angle formed with the x- axis or y axis ,then direction is given by
θ = [tex]tan^{-1}\frac{b}{a}[/tex]
According to the given question
We have
Position vector (6, 5.2)
So, the magnitude of the position vector = [tex]\sqrt{6^{2}+(5.2)^{2} }[/tex] = [tex]\sqrt{36+27.04}[/tex]
= [tex]\sqrt{63.04} =7.93[/tex]
Now, the direction angle of the vector is given by
[tex]tan\alpha =\frac{6}{5.2} \\ tan\alpha =1.15\\\alpha =tan^{-1} (1.5) = 56degrees.[/tex]
Therefore,
θ = 90 -56 = 34degrees.
Hence, the direction angle and magnitude of the position vector are 34degrees and 7.93 respectively.
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