Given vector $vecA=2hati + 1hatj$ and vector $vecB=3hatj$ , how do you find the component of $vecA$ in the direction of $vecB$ ?

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Answer 1 · 2017-04-15T00:20:46

Please read the vector projection reference and then please read the explanation.

Compute unit vector in the direction of $vecB$ :

$hatB = vecB/(|vecB|)$

$|vecB|= sqrt(0^2+3^2)$

$|vecB|= 3$

$hatB = (3hatj)/3$

$hatB = 1hatj$

Let $vecA_B =$ the projection of $vecA$ in the direction of $vecB$

$vecA_B = (vecA*vecB)/|vecB|(hatB)$

$vecA*vecB = (2)(0)+(1)(3) = 3$

$vecA_B = (3)/3(hatj)$

$vecA_B = hatj$

The would be more instructional, if $vecB$ had a non-zero $hati$ component but I hope that this helps.

Given vector vecA=2hati + 1hatjvecA=2hati + 1hatj and vector vecB=3hatjvecB=3hatj, how do you find the component of vecAvecA in the direction of vecBvecB?