Question

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

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

For what value of λ are the vectors $\stackrel{\wedge}{i}+2λ \stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $2\stackrel{\wedge}{i}+\stackrel{\wedge}{j} -3\stackrel{\wedge}{k}$ perpendicular ?

Find a unit vector in the direction of $\stackrel{\rightarrow}{A}$ = $3\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +6\stackrel{\wedge}{k}$

Write the value of $\stackrel{\rightarrow}{p}\$ for which the vectors $3\stackrel{\wedge}{i}+2\stackrel{\wedge}{j} +9\stackrel{\wedge}{k}$ and $\stackrel{\wedge}{i}-2p\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ are parallel vectors.

Write the projection of the vector $\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ along the vector $\stackrel{\rightarrow}{j}\$.

Write a unit vector in the direction of the sum of vectors : $\stackrel{\rightarrow}{a}\ = 2\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +2\stackrel{\wedge}{k} and \stackrel{\rightarrow}{b}\ = \stackrel{\wedge}{i}+\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$