Question

If abar =2i+3j+and b bar =2j +3k the component b bar. Along a bar

Answer 1

Answer:

6/√13

Explanation:

Given

The vectors are given as

⃗A = 2i + 3j

⃗B = 2j + 3k

Concept

Component of a vector ⃗b along another vector ⃗a is given by

| ⃗bₐ | = |⃗b|cos(θ), θ is angle between ⃗a and ⃗b

⇒ | ⃗bₐ | = |⃗b|cos(θ)*|⃗a|/|⃗a|

⇒ | ⃗bₐ | = |⃗a||⃗b|cos(θ)/|⃗a|

⇒ | ⃗bₐ | = ( ⃗a.⃗b)/|⃗a|

Calculation

|⃗A| = √(2²+3²) = √(4+9) =√13

⃗A.⃗B = (2i + 3j).(2j + 3k)

= 4i.j + 6i.k + 6j.j + 9j.k

= 0 + 0 + 6 + 0

= 6

|⃗Bₐ | = ( ⃗A.⃗B)/|⃗A|

= 6/√13