Mag and Direction of 3d Vectors

Thread starter Loppyfoot
Start date Oct 12, 2009
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3d Direction Vectors

AI Thread Summary

To find the magnitude and direction of the vector C = -2i - 9j + 4k, the magnitude is calculated as 10 using the formula √(x² + y² + z²). To determine the angle from the +z-axis, the formula involves using the z-component (4) divided by the magnitude (10). For the direction in the xy-plane, the angle can be found using the arctangent of the y-component (-9) over the x-component (-2), with adjustments made for the correct quadrant. The discussion seeks clarity on these calculations and the specific formulas needed for angles. Understanding these concepts is essential for solving 3D vector problems effectively.

Oct 12, 2009

Loppyfoot

Homework Statement

Find the magnitude and direction of the following vectors.
C = -2 i - 9 j + 4 k

I found that the magnitude was 10. By using the square root of (4+9+4).

I don't know how to find:
Angle from +z-axis
and the direction in xy plane counter clockwise from the +x axis.

Thanks

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Oct 12, 2009

dtrain121

gamma=Az divided by A

Oct 12, 2009

Loppyfoot

English please? is Az, 4k? Also, how do I find the direction in xy plane counter clockwise from the +x axis?

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