Tag: scalars and vectors

Questions Related to scalars and vectors

What is the distance in space between $(1,0,5)$ and $(-3,6,3)$?

maths introduction to three dimensional geometry distance between two points in 3d distance between two points in space scalars and vectors

  1. $4$

  2. $6$

  3. $2\sqrt { 11 } $

  4. $2\sqrt { 14 } $

  5. $12$

Show answer
Correct Option: D
Explanation:

The distance between the points $(1,0,5)$ and $(-3,6,3)$ is given below:

$D=\sqrt { \left( 3-5 \right) ^{ 2 }+\left( 6-0 \right) ^{ 2 }+\left( -3-1 \right) ^{ 2 } } $
$=\sqrt { \left( -2 \right) ^{ 2 }+\left( 6 \right) ^{ 2 }+\left( -4 \right) ^{ 2 } } $
$=\sqrt { 4+36+16 } =\sqrt { 56 } $
$=2\sqrt { 14 }$ 

$L _1:\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}$
$L _2:\dfrac{x-2}{3}=\dfrac{y-4}{2}=\dfrac{z-5}{5}$ be two given lines, point P lies on $L _1$ and Q lies on $L _2$ then distance between P and Q can be

maths introduction to three dimensional geometry distance between two points in 3d distance between two points in space scalars and vectors

  1. $\dfrac{1}{3}$

  2. $\dfrac{1}{9}$

  3. $15$

  4. $30$

Show answer
Correct Option: A,C,D
Explanation:

$\dfrac{|\begin{vmatrix}2-1&4-2  &5-3 \2 & 3 &4 \ 3& 2 & 5\end{vmatrix}|}{|\begin{vmatrix}i&j  &k \2 & 3 & 4\3 & 2 & 5\end{vmatrix}|}=\dfrac{1}{\sqrt{78}}$