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Numerade Educator

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Problem 44 Easy Difficulty

Find the scalar and vector projections of $ b $ onto $ a $.

$ a = i + 2j + 3k $ , $ b = 5i - k $

Answer

scalar projection b onto a $=\frac{2}{\sqrt{14}}$ vector projection $=\frac{2}{14} i+\frac{4}{14} j+\frac{6}{14} k$

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Video Transcript

Hello. We have a question in this we need to find the scalar and vector projection of be onto a for a victories. I kept bless to Jacob bless three K cap and be vector is five. I kept minus take up. Now we know that scalar projection of Okay, lets projection of but B on two A is always be dot A divided by the magnitude of evicted and the victim protection. The victor prediction of B on e equals two be dot a by magnitude of a whole square B dot by a magnitude of a called square and in multiplied by a victor. Okay mm Okay, okay. No will be using this formula this formula to find the projection no projections of skilled skilled projection of projection of B on A will be into a B dot means BS five. I kept minus kate camp and today is a victories I kept Plus two J camp place three K cap. Development magnitude of ah evicted magnitude of a vector will be one is squared plus two squared plus three square under the square root. No, this is I and I. So we have dot product has five into 1 Plus -1 into zero, blessed minus one into uh three. Here it should be, it should be zero into to divide by nine plus 4, 13 plus 1, 14 and uh oh So this will be 5 -3 Dubai 14 and the root. Okay and if you want to replace it We have to multiply and divide with under 14. So this would be 214 5, 14, seven. So answer that there could be Dubai under 14, art Under 14 x seven. This is the scared product. Uh Sorry sorry. Scale production of beyond 2nd is the vector projection that production of B on in a turn directed. This is equal to be dot A by a magnitude hold square. So be dot meant five I -K. Dot A. I. Plus do J. Mystery K. But magnitude of uh victor whole square. Uh huh. And the route 14 whole spread into evicted victories. I plus do J. It's tricky. So this will be five and 25 -3 by 14 and I can't Plus two. J. Camp last three gap. Okay, so five minutes three is too to have 14. One by seven. I care plus do their cab. There's three Cape gaps. They should be the answer. Thank you.