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
[tex]\overrightarrow{v_{a}}=\widehat{i}-2\widehat{j}+\widehat{k}[/tex]
Similarly vector B is written as
[tex]\overrightarrow{v_{b}}=4\widehat{i}-4\widehat{j}+7\widehat{k}[/tex]
Thus the vector dot product of the 2 vectors is obtained as
[tex]\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[/tex]
Part 2)
Given vector A' as
[tex]\overrightarrow{v_{a'}}=2\widehat{i}+3\widehat{j}+6\widehat{k}[/tex]
Similarly vector B' is written as
[tex]\overrightarrow{v_{b'}}=\widehat{i}+5\widehat{j}+3\widehat{k}[/tex]
Thus the vector dot product of the 2 vectors is obtained as
[tex]\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[/tex]
