Quiz about Three Dimensional Geometry

Question 1

$$P$$ is a point on the line joining the points $$A(0,5,-2)$$ and $$B(3,-1,2)$$. If the $$x$$-coordinate of $${P}$$ is 6 , then its $${z}$$-coordinate is

Accepted Answer

Covalent bond

Answer

$$6$$

Answer

$$10$$

Answer

$$-6$$

Answer

$$-10$$

Question 2

Assertion (A): The acute angle between the line $$\bar{r}=\hat{i}+\hat{i}+2 \hat{k}+\lambda(\hat{i}-\hat{j})$$ and the $${x}$$-axis is $$\frac{\pi}{4}$$

Reason(R): The acute angle $$	heta$$ between the lines

$$\bar{r}=x_1 \hat{i}+y_1 \hat{j}+z_1\hat{k}+\lambda(a_1 \hat{i}+b_1 \hat{j}+c_1\hat{k})$$ and

$$\bar{r}=x_2 \hat{i}+y_2 \hat{j}+z_2 \hat{k}+\mu(a_2 \hat{i}+b_2 \hat{j}+c_2 \hat{k})$$

is given by

$$\cos 	heta=\frac{|a_1 a_2+b_1 b_2+c_1 c_2|}{\sqrt{a_1{ }^2+b_1{ }^{2}+c_1{ }^{2}} \sqrt{a_2{ }^{2}+b_2{ }^{2}+c_2{ }^{2}}}$$

Accepted Answer

Covalent bond

Answer

Both $${A}$$ and $${R}$$ are true and $${R}$$ is the correct explanation of $${A}$$.

Answer

Both $${A}$$ and $${R}$$ are true but $${R}$$ is not the correct explanation of $${A}$$.

Answer

A is true but $$R$$ is false.

Answer

A is false but $${R}$$ is true.

Question 3

![](http://admin.getprephub.com/media/editor/Screenshot%202022-10-11%20162333_20221011141529061646.png)

Accepted Answer

Covalent bond

Answer

$$9 	ext { units }$$

Answer

$$10 	ext { units }$$

Answer

$$11 	ext { units }$$

Answer

$$12 	ext { units }$$

Question 4

The equations of motion of a rocket are:
$$x=2 t, y=-4 t, z=4 t$$, where the time $$t$$ is given in seconds, and the coordinates of a moving point in $${km}$$. What is the path of the rocket? At what distances will the rocket be from the starting point $${O}(0,0,0)$$ and from the following line in 10 seconds?

$$\vec{r}=20 \hat{i}-10 \hat{j}+40 \hat{k}+\mu(10 \hat{i}-20 \hat{j}+10 \hat{k})$$

Accepted Answer

Covalent bond

Answer

$$10 \sqrt{3} k m$$

Answer

$$80 \sqrt{2} k m$$

Answer

$$18 \sqrt{5} k m$$

Answer

$$50 \sqrt{7} k m$$

Three Dimensional Geometry Cbse Class 12 Maths Problems and Solutions

Many students find Three Dimensional Geometry for Cbse Class 12 particularly challenging. Strengthen your concepts and gain confidence for your exams by solving free questions for Three Dimensional Geometry from for Cbse Class 12 preparation.