A vector $\vec{X}$ , when added to the resultant of the vectors $\vec{A}$ = 3î - 5ĵ +7k̂ and $\vec{B}$ = 2î + 4ĵ - 3k̂ gives a unit vector along Y axis , Find the vector $\vec{X}$

Question

Question

Answer 1

option(1)

CONCEPT:

Vector has both magnitude and direction, so they cannot be added by using the ordinary rule of algebra.
- Vectors can be added geometrically by the vector law of addition.

Vector Law of Addition state that R = $\vec{A} + \vec{B}$

F20 Jitendra K 3-6-2021 Swati D10

EXPLANATION:

Resultant of $\vec{A}$ and $\vec{B}$ is

According to the vector law of addition

R= $\vec{A} + \vec{B}$ where $\vec{A}$ = 3î -5ĵ +7k̂ and $\vec{B}$ = 2î +4ĵ-3k̂ on putting the value we get

R= (3î -5ĵ +7k̂ ) + (2î +4ĵ-3k̂) = -5î +2ĵ-4k̂ .............................(i)

Unit vector along Y axis = ĵ

So the required vector

$\vec{X}$ = Ĵ - $\vec{R}$ , ĵ -(5î -ĵ +4k̂) where (R = 5î -ĵ +4k̂ ) = -5î + 2ĵ - 4k̂

Hence the vector $\vec{X}$ will be -5î +2ĵ -4k̂