Question

Pls answer this question
Below
Pls explain too I am not good at vectors

Answer 1

concept :- component of A along B is given by
$\frac{\vec{A}.\vec{B}}{|B|}$

(i) A = i - 2j and B = 2i + 3k
A + B = (i - 2j ) + (2i + 3k) = 3i - 2j + 3k
we have to find component of (A + B) along x-axis
so, component = (A + B).i/|i|
= (3i - 2j + 3k).i/1
= 3 × 1 - 2 × 0 + 3 × 0
= 3


(ii) A + B = 3i - 2j + 3k and C = i + j
we have to find component of (A+ B) along C.
component = (A + B).C/|C|
= (3i - 2j + 3k).(i + j)/√(1² + 1²)
= (3 - 2)/√2
= 1/√2