Could you point where B cos θ and Bx in the following diagram?
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Dr.Peterson
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Draw a vertical line down from the head of arrow B to meet the x axis at a point we'll call X.
Bx is the x-coordinate (component) of vector B, which is the distance along the x-axis from the origin O to point X.
Looking at the right triangle OBX, you can see that that same distance, Bx, is |B|cos(θ), because cos(θ) is the ratio of that horizontal distance to the length of the hypotenuse, |B|.
Steven G
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B cosθ and Bx are the same. They are the projection of B onto the x-axis
mmm4444bot
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In the following diagram, the sun shines down from above, and the "top" vector casts a gray shadow onto the "bottom" vector.
In your diagram, the top vector is B and the bottom vector is A.
Vector B casts a shadow onto vector A. We call this shadow the "projection of B onto A".
We name the projection's length Bx and we calculate its value as |B|⋅cos(θ)
In your diagram, the top vector is B and the bottom vector is A.
Vector B casts a shadow onto vector A. We call this shadow the "projection of B onto A".
We name the projection's length Bx and we calculate its value as |B|⋅cos(θ)