Q.
$ P (0,3,-2) ; Q (3,7,-1)$ and $R (1,-3,-1)$ are 3 given points. Let $L _1$ be the line passing through $P$ and $Q$ and $L_2$ be the line through $R$ and parallel to the vector ${V}=\hat{ i }+\hat{ k }$
Column I
Column II
A
perpendicular distance of $P$ from $L _2$
P
$7 \sqrt{3}$
B
shortest distance between $L _1$ and $L _2$
Q
2
C
area of the triangle $PQR$
R
6
D
distance from $(0,0,0)$ to the plane $P Q R$
S
$\frac{19}{\sqrt{147}}$
| Column I | Column II | ||
|---|---|---|---|
| A | perpendicular distance of $P$ from $L _2$ | P | $7 \sqrt{3}$ |
| B | shortest distance between $L _1$ and $L _2$ | Q | 2 |
| C | area of the triangle $PQR$ | R | 6 |
| D | distance from $(0,0,0)$ to the plane $P Q R$ | S | $\frac{19}{\sqrt{147}}$ |
Vector Algebra
Solution: