Find the vector projv u.
-v = k, u = 9i + 2j + 6k
A) $\frac { 54 } { 121 } \mathbf { i } + \frac { 12 } { 121 } \mathbf { j } + \frac { 36 } { 121 } \mathbf { k }$
B) $\frac { 54 } { 11 } \mathbf { i } + \frac { 12 } { 11 } \mathbf { j } + \frac { 36 } { 11 } \mathbf { k }$
C) $\frac { 6 } { 121 } \mathbf { k }$
D) $6 \mathbf { k }$

Question

Find the vector projv u.
-v = k, u = 9i + 2j + 6k 
A) $\frac { 54 } { 121 } \mathbf { i } + \frac { 12 } { 121 } \mathbf { j } + \frac { 36 } { 121 } \mathbf { k }$
B) $\frac { 54 } { 11 } \mathbf { i } + \frac { 12 } { 11 } \mathbf { j } + \frac { 36 } { 11 } \mathbf { k }$
C) $\frac { 6 } { 121 } \mathbf { k }$
D) $6 \mathbf { k }$

Quizplus · Accepted Answer

The projection of $\mathbf{u}$ onto $\mathbf{v}$ (where $\mathbf{v} = \mathbf{k}$) is calculated using the formula $\text{proj}_{\mathbf{v}} \mathbf{u} = \frac{\mathbf{u} \cdot \mathbf{v}}{\|\mathbf{v}\|^2} \mathbf{v}$. Since $\mathbf{v} = \mathbf{k}$, its dot product with $\mathbf{u} = 9\mathbf{i} + 2\mathbf{j} + 6\mathbf{k}$ is $6$, and $\|\mathbf{v}\|^2 = 1$, so the projection is $6\mathbf{k}$.

Find the Vector Projv U 54121i+12121j+36121k\frac { 54 } { 121 } \mathbf { i } + \frac { 12 } { 121 } \mathbf { j } + \frac { 36 } { 121 } \mathbf { k }12154​i+12112​j+12136​k

Find the Vector Projv U $\frac { 54 } { 121 } \mathbf { i } + \frac { 12 } { 121 } \mathbf { j } + \frac { 36 } { 121 } \mathbf { k }$