Question

The component of a vector r along X-axis will have maximum value if...
(a) r is along positive Y-axis
(b) r is along positive X-axis
(c) r makes an angle of 45° with the X-axis
(d) r is along negative Y-axis

pls answer stepwise with reason...​

Answer 1

answer : option (b) r is along positive X-axis.

explanation : we know, if two vectors a and b are given,

then, component of a along the direction of b = |a|cosα, where α is angle made between a and b.

similarly, component of b along the direction of a = |b|cosα.

Let vector r makes an angle β with x-axis. then, component of vector r along the direction of x-axis = |r|cosβ

now plz tell me, when |r|cosβ will be maximum.

yes of course , when β = 0°

it means,component of a vector r along X-axis will have maximum value if r is along positive x - axis