Question

If `vec"A" = (2hat"i"+3hat"j"- hat"k")`m and `vec"B" = (hat"i" + 2hat"j"+ 2hat"k")` m. The magnitude of component of vector `vec"A"` along vector `vec"B"` will be ______ m. 

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Answer 1

If `vec"A" = (2hat"i"+3hat"j"- hat"k")`m and `vec"B" = (hat"i" + 2hat"j"+ 2hat"k")` m. The magnitude of component of vector `vec"A"` along vector `vec"B"` will be 2 m. 

Explanation:

Given that

`vec"A" = (2hat"i"+3hat"j"- hat"k")` m and `vec"B" = (hat"i" + 2hat"j"+ 2hat"k")` m

Component of vector `vec"A"` along vector `vec"B"=vec"A".vec"B"`

= `(vec"A".vec"B")/|vec"B"| = (2+6-2)/(sqrt(1^2+2^2+2^2))`    `(∵hat"B"=vec"B"/|vec"B"|)`

= `6/3`

= 2 m