Three Dimensional Geometry: 1 mark Questions (CBSE Class 12)

The length of perpendicular drawn from point (2, 5, 7) on line $\frac{x}{1}=\frac{y}{0}=\frac{z}{0}$ is

1. (A)2
2. (B)5
3. (C)$\sqrt{74}$
4. (D)$\sqrt{78}$

Assertion (A): Lines given by $x=py+q,z=ry+s$ and $x=p^{\prime }y+q^{\prime },z=r^{\prime }y+s^{\prime }$ are perpendicular to each other when $p{p}^{\prime }+r{r}^{\prime }=1$.
Reason (R): Two lines $\vec{r}={\vec{a}}_1+\lambda {\vec{b}}_1$ and $\vec{r}={\vec{a}}_2+\mu {\vec{b}}_2$ are perpendicular to each other if ${\vec{b}}_1\cdot {\vec{b}}_2=0$.

1. (A)Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true and Reason (R) is false.
4. (D)Assertion (A) is false and Reason (R) is true.

The length of perpendicular drawn from the point (1, 2, 3) on line $\frac{x}{0}=\frac{y}{1}=\frac{z}{0}$ is

1. (A)2
2. (B)6
3. (C)$\sqrt{10}$
4. (D)$\sqrt{14}$

The length of perpendicular drawn from the point (3, 4, 2) on the line $\frac{x}{0}=\frac{y}{0}=\frac{z}{1}$ is

1. (A)2
2. (B)9
3. (C)5
4. (D)$\sqrt{29}$

Direction cosines of the line given by equations : $\frac{2x-1}{4}=\frac{1-y}{3}=\frac{-z}{6}$ are

1. (A)$2,-3,-6$
2. (B)$\frac{2}{7},\frac{-3}{7},\frac{-6}{7}$
3. (C)$\frac{2}{7},\frac{-3}{7},\frac{6}{7}$
4. (D)$\frac{4}{\sqrt{61}},\frac{-3}{\sqrt{61}},\frac{-6}{\sqrt{61}}$

Assertion (A) : A line can have direction cosines $<1,1,1>$
Reason (R) : $\cos \theta =1$ is possible for $\theta =0$.

1. (A)Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

Direction cosines of line $x=y=1-z$ are

1. (A)$1,1,1$
2. (B)$\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{-1}{\sqrt{3}}$
3. (C)$0,0,1$
4. (D)$\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$

Direction cosines of line $\frac{1-x}{0}=y=z$ are

1. (A)$1,1,1$
2. (B)$0,\frac{-1}{\sqrt{2}},\frac{-1}{\sqrt{2}}$
3. (C)$1,0,0$
4. (D)$0,-1,-1$

If $l_1,m_1,n_1$ and $l_2,m_2,n_2$ are direction cosines of lines $L_1$ and $L_2$ respectively and $\theta$ is the acute angle between them, then :

1. (A)$\cos \theta =l_1{l}_2+m_1{m}_2+n_1{n}_2$
2. (B)$\sin \theta =l_1{l}_2+m_1{m}_2+n_1{n}_2$
3. (C)$\tan \theta =\frac{l_1}{l_2}+\frac{m_1}{m_2}+\frac{n_1}{n_2}$
4. (D)$\cos \theta =|l_1{l}_2+m_1{m}_2+n_1{n}_2|$

Direction ratios of lines $l_1$ and $l_2$ are $⟨12,-3,9⟩$ and $⟨4,q,-p⟩$ respectively. The values of p and q for which $l_1$ and $l_2$ are parallel are respectively :

1. (A)$-1,3$
2. (B)$3,1$
3. (C)$-3,-1$
4. (D)$-1,-3$

Direction ratios of lines $l_1$ and $l_2$ respectively are $⟨1,-2,3⟩$ and $⟨-2,p,-6⟩$. The value of p for which $l_1\parallel l_2$, is :

1. (A)$-4$
2. (B)$4$
3. (C)$-10$
4. (D)$10$

Direction ratios of lines $l_1$ and $l_2$ respectively are $⟨1,0,0⟩$ and $⟨0,-1,0⟩$. The direction ratios of the line perpendicular to both $l_1$ and $l_2$ are :

1. (A)$⟨1,1,0⟩$
2. (B)$⟨0,0,-1⟩$
3. (C)$⟨1,1,1⟩$
4. (D)$⟨1,0,-1⟩$