Question

Write the projection of the vector $\stackrel{\rightarrow}{a}\$ = $2\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ on the vector $\stackrel{\rightarrow}{b}\$ = $\stackrel{\wedge}{i}+2\stackrel{\wedge}{j} +2\stackrel{\wedge}{k}$.

Find the projection of vector $\stackrel{\rightarrow}{a}\$ = $2\stackrel{\wedge}{i}+3\stackrel{\wedge}{j} +2\stackrel{\wedge}{k}$ on the vector $\stackrel{\rightarrow}{b}\$ = $2\stackrel{\wedge}{i}+2\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$

Find a vector of magnitude 5 units and parallel to the resultant of $\stackrel{\rightarrow}{a}\$ = $2\stackrel{\wedge}{i}+3\stackrel{\wedge}{j} -\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}\$ = $\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$.

Find ‘λ’ when the projection of $\stackrel{\rightarrow}{a}\$ = $λ\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ on $\stackrel{\rightarrow}{b}\$ = $2\stackrel{\wedge}{i}+6\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ is 4 units.

Find $\stackrel{\rightarrow}{a}$.$\stackrel{\rightarrow}{b}$,If $\stackrel{\rightarrow}{a}$ = $-\stackrel{\wedge}{i}+\stackrel{\wedge}{j} -2\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}$ = $2\stackrel{\wedge}{i}+3\stackrel{\wedge}{j} -\stackrel{\wedge}{k}$.

Find a unit vector parallel to the sum of vectors $\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +5\stackrel{\wedge}{k}$

Write the projection of the vector $7\stackrel{\wedge}{i}+\stackrel{\wedge}{j} -4\stackrel{\wedge}{k}$ on the vector $2\stackrel{\wedge}{i}+6\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$.