Question

The component of a vector r along X-axis will have maximum value if ______.

विकल्प

• 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

Answer 1

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.