The vector projection of $\mathbf { v } = 0$ onto $\mathbf { w } = 2 \mathbf { i } + \mathbf { j } - 3 \mathbf { k }$ is

A) $2 \mathbf { i } + \mathbf { j } - 3 \mathbf { k }$
B) $0 \mathbf { i } + 0 \mathbf { j } + 0 \mathbf { k }$
C) $\frac { 2 } { 14 } i + \frac { 1 } { 14 } \mathbf { j } - \frac { 3 } { 14 } \mathbf { k }$
D) $- \frac { 2 } { 14 } \mathbf { i } - \frac { 1 } { 14 } \mathbf { j } + \frac { 3 } { 14 } \mathbf { k }$
E)Undefined

Question

The vector projection of $\mathbf { v } = 0$ onto $\mathbf { w } = 2 \mathbf { i } + \mathbf { j } - 3 \mathbf { k }$ is

A) $2 \mathbf { i } + \mathbf { j } - 3 \mathbf { k }$
B) $0 \mathbf { i } + 0 \mathbf { j } + 0 \mathbf { k }$
C) $\frac { 2 } { 14 } i + \frac { 1 } { 14 } \mathbf { j } - \frac { 3 } { 14 } \mathbf { k }$
D) $- \frac { 2 } { 14 } \mathbf { i } - \frac { 1 } { 14 } \mathbf { j } + \frac { 3 } { 14 } \mathbf { k }$
E)Undefined

Quizplus · Accepted Answer

The vector projection of a zero vector onto any other vector is always the zero vector itself, because the zero vector has no direction or magnitude to project.

The Vector Projection Of v=0\mathbf { v } = 0v=0 Onto w=2i+j−3k\mathbf { w } = 2 \mathbf { i } + \mathbf { j } - 3 \mathbf { k }w=2i+j−3k

The Vector Projection Of $\mathbf { v } = 0$ Onto $\mathbf { w } = 2 \mathbf { i } + \mathbf { j } - 3 \mathbf { k }$