Question

If A=2i+3j and B=2j+3k , the component of B along A is

Answer 1

6/√13

Explanation:

Given,

A=2i+3j+0k, and B=0i+2j+3k, then

|A| = √{(2)²+(3)²+(0)²} = √(4+9+0) = √13

|B| = √{(0)²+(2)²+(3)²} = √(0+4+9) = √13

A.B = (2i+3j+0k).(0i+2j+3k) = 2x0+3x2+0x3

= 0+6+0 = 6

we know that,

A.B = |A|.|B|.CosØ

6 = √13.√13.CosØ

6 = 13.CosØ

CosØ = 6/13

Now,

the component of B along A = |B|.CosØ

= √13x6/13 = 6/√13.