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Question
The component of a vector r along X-axis will have maximum value if ______.
Options
r is along positive Y-axis
r is along positive X-axis
r makes an angle of 45° with the X-axis
r is along negative Y-axis
Solution
The component of a vector r along X-axis will have maximum value if r is along positive X-axis.
Explanation:
Consider a vector `vecR` in X - Y plane as shown in the figure. If we draw orthogonal vectors `vecR_x` and `vecR_y` along x and y axes respectively, by law of vector addition, `vecR = vecR_x + vecR_y`
The magnitude of component of r along the X-axis
`r_x = |r| cos theta`
`(r_x)_"maximum" = |r| (cos theta)_"maximum"`
`r_x = |r| cos theta`
= `|r| cos 0°`
= `|r|` .....(∵ cos θ is maximum if θ = 0°)
As θ = 0°,
r is along the positive x-axis.
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