3D Geometry

$\cos^{-1}\left( \dfrac{1}{9} \right)$

$\cos^{-1}\left( \dfrac{4}{9} \right)$

$\cos^{-1}\left( \dfrac{2}{9} \right)$

$\cos^{-1}\left( \dfrac{3}{9} \right)$

$x+2=0$

$y-3=0$

$z=3$

$x-2=0$

$\dfrac{x+3}{-3}=\dfrac{y+4}{5}=\dfrac{z-7}{8}$

$\dfrac{x-3}{-3}=\dfrac{y-4}{5}=\dfrac{z+7}{8}$

$\dfrac{x+3}{3}=\dfrac{y+4}{-5}=\dfrac{z-7}{8}$

$\dfrac{x-3}{3}=\dfrac{y-4}{-5}=\dfrac{z+7}{8}$

1

2

0

3

$\bar{r}=(4 \hat{i}-2 \hat{j}+3 \hat{k})+\lambda(\hat{i}+\hat{k})$

$\bar{r}=(4 \hat{i}-2 \hat{j}+3 \hat{k})+\lambda(\hat{i})$

$\bar{r}=(4 \hat{i}-2 \hat{j}+3 \hat{k})+\lambda(\hat{j})$

$\bar{r}=(4 \hat{i}-2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{k})$

$\dfrac{x-a}{b}=y=\dfrac{z-c}{d}$

$\dfrac{x-b}{a}=\dfrac{y-d}{c}=z$

$x=\dfrac{y-a}{b}=\dfrac{z-c}{d}$

$\dfrac{x-b}{a}=y=\dfrac{z-d}{c}$

$y=1, z=1$

$x=0$

$x+y+z=2$

$y=z$

$\dfrac{1}{2}$

2

$\dfrac{5}{2}$

$\dfrac{7}{2}$

two straight lines

a pair of straight lines passing through the origin

2 planes parallel to YZ -plane

2 planes parallel to $X Z^{-}$-plane

15

-7

7

-5

$(-4\overset{\hat{}}{i}-2\overset{\hat{}}{j}-\overset{\hat{}}{k})+\lambda(2\overset{\hat{}}{i}+3\overset{\hat{}}{j}-2\overset{\hat{}}{k})$

$(4\overset{\hat{}}{i}+2\overset{\hat{}}{j}+\overset{\hat{}}{k})+\lambda(-2\overset{\hat{}}{i}-3\overset{\hat{}}{j}+2\overset{\hat{}}{k})$

$(-4\overset{\hat{}}{i}-2\overset{\hat{}}{j}-\overset{\hat{}}{k})+\lambda(2\overset{\hat{}}{i}+3\overset{\hat{}}{j}-4\overset{\hat{}}{k})$

$(4\overset{\hat{}}{i}+2\overset{\hat{}}{j}+\overset{\hat{}}{k})+\lambda(-2\overset{\hat{}}{i}-3\overset{\hat{}}{j}+4\overset{\hat{}}{k})$

1 unit

2 units

3 units

4 units

2

5

3

7

$\dfrac{\pi}{6}$

$\cos^{-1}\left( \dfrac{7}{18} \right)$

$\cos^{-1}\left( \dfrac{1}{18} \right)$

$\dfrac{\pi}{3}$

5

3

4

2