Answer:
![\frac{4x^2z^4}{9y^2}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%5E2z%5E4%7D%7B9y%5E2%7D)
Step-by-step explanation:
Answer:
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Answer:
Part 1)
Projection of vector A on vector B equals 19 units
Part 2)
Projection of vector B' on vector A' equals 35 units
Step-by-step explanation:
For 2 vectors A and B the projection of A on B is given by the vector dot product of vector A and B
Given
![\overrightarrow{v_{a}}=\widehat{i}-2\widehat{j}+\widehat{k}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_%7Ba%7D%7D%3D%5Cwidehat%7Bi%7D-2%5Cwidehat%7Bj%7D%2B%5Cwidehat%7Bk%7D)
Similarly vector B is written as
![\overrightarrow{v_{b}}=4\widehat{i}-4\widehat{j}+7\widehat{k}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_%7Bb%7D%7D%3D4%5Cwidehat%7Bi%7D-4%5Cwidehat%7Bj%7D%2B7%5Cwidehat%7Bk%7D)
Thus the vector dot product of the 2 vectors is obtained as
![\overrightarrow{v_{a}}\cdot \overrightarrow{v_{b}}=(\widehat{i}-2\widehat{j}+\widehat{k})\cdot (4\widehat{i}-4\widehat{j}+7\widehat{k})\\\\\overrightarrow{v_{a}}\cdot \overrightarrow{v_{b}}=1\cdot 4+2\cdot 4+1\cdot 7=19](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_%7Ba%7D%7D%5Ccdot%20%5Coverrightarrow%7Bv_%7Bb%7D%7D%3D%28%5Cwidehat%7Bi%7D-2%5Cwidehat%7Bj%7D%2B%5Cwidehat%7Bk%7D%29%5Ccdot%20%284%5Cwidehat%7Bi%7D-4%5Cwidehat%7Bj%7D%2B7%5Cwidehat%7Bk%7D%29%5C%5C%5C%5C%5Coverrightarrow%7Bv_%7Ba%7D%7D%5Ccdot%20%5Coverrightarrow%7Bv_%7Bb%7D%7D%3D1%5Ccdot%204%2B2%5Ccdot%204%2B1%5Ccdot%207%3D19)
Part 2)
Given vector A' as
![\overrightarrow{v_{a'}}=2\widehat{i}+3\widehat{j}+6\widehat{k}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_%7Ba%27%7D%7D%3D2%5Cwidehat%7Bi%7D%2B3%5Cwidehat%7Bj%7D%2B6%5Cwidehat%7Bk%7D)
Similarly vector B' is written as
![\overrightarrow{v_{b'}}=\widehat{i}+5\widehat{j}+3\widehat{k}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_%7Bb%27%7D%7D%3D%5Cwidehat%7Bi%7D%2B5%5Cwidehat%7Bj%7D%2B3%5Cwidehat%7Bk%7D)
Thus the vector dot product of the 2 vectors is obtained as
![\overrightarrow{v_{b'}}\cdot \overrightarrow{v_{a'}}=(\widehat{i}+5\widehat{j}+3\widehat{k})\cdot (2\widehat{i}+3\widehat{j}+6\widehat{k})\\\\\overrightarrow{v_{a'}}\cdot \overrightarrow{v_{b'}}=1\cdot 2+5\cdot 3+3\cdot 6=35](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_%7Bb%27%7D%7D%5Ccdot%20%5Coverrightarrow%7Bv_%7Ba%27%7D%7D%3D%28%5Cwidehat%7Bi%7D%2B5%5Cwidehat%7Bj%7D%2B3%5Cwidehat%7Bk%7D%29%5Ccdot%20%282%5Cwidehat%7Bi%7D%2B3%5Cwidehat%7Bj%7D%2B6%5Cwidehat%7Bk%7D%29%5C%5C%5C%5C%5Coverrightarrow%7Bv_%7Ba%27%7D%7D%5Ccdot%20%5Coverrightarrow%7Bv_%7Bb%27%7D%7D%3D1%5Ccdot%202%2B5%5Ccdot%203%2B3%5Ccdot%206%3D35)
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