Given three points P(1, -1, 0), Q(0, 1, 2) and R(-1, -1, 1), find the distance from the point Q to the line passing through the points P and R.
A) $\sqrt { 29 }$
B) $\sqrt { \frac { 29 } { 5 } }$
C) $\sqrt { \frac { 29 } { 6 } }$
D) $\frac { \sqrt { 29 } } { 3 }$
E) $\frac { 1 } { \sqrt { 29 } }$
F) $\sqrt { \frac { 5 } { 29 } }$
G) $\sqrt { \frac { 6 } { 29 } }$
H) $\frac { 3 } { \sqrt { 29 } }$

Question

Given three points P(1, -1, 0), Q(0, 1, 2) and R(-1, -1, 1), find the distance from the point Q to the line passing through the points P and R.
A) $\sqrt { 29 }$ 
B) $\sqrt { \frac { 29 } { 5 } }$ 
C) $\sqrt { \frac { 29 } { 6 } }$ 
D) $\frac { \sqrt { 29 } } { 3 }$ 
E) $\frac { 1 } { \sqrt { 29 } }$ 
F) $\sqrt { \frac { 5 } { 29 } }$ 
G) $\sqrt { \frac { 6 } { 29 } }$ 
H) $\frac { 3 } { \sqrt { 29 } }$

Quizplus · Accepted Answer

The distance from a point to a line can be found using the formula involving the cross product of vectors and the distance formula. Here, we first find the vector $\vec{PR}$ and the vector $\vec{PQ}$, then use them to find the area of the parallelogram they span (which is the magnitude of their cross product), and finally use the area of a parallelogram formula $A = base \times height$ to solve for the height, which represents the distance from point $Q$ to the line through $P$ and $R$. The correct calculation leads to $\sqrt{\frac{29}{5}}$, making option B the correct answer.

Given Three Points P(1, -1, 0), Q(0, 1, 2) and R(-1