Introduction to Three Dimensional Geometry Test

Result

Introduction to Three Dimensional Geometry Test - 33

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

If the point $$ A(3, -2, 4), B(1, 1, 1) $$ and $$ C(-1, 4, -2) $$ are collinear then $$ (C : AB) $$

A
$$1 : 2$$

B
$$-2 : 1$$

C
$$-1 : 2$$

D
$$4 : 0$$

Solution
Question 2
1 / -0

Centroid of triangle formed by foot of perpendiculars from (-3, -6, -9) on coordinate axes is:-

A
(-1, -2, -3)

B
(1, 2, 3)

C
(1, -2, -3)

D
(-1, -2, 3)

Solution
Question 3
1 / -0

If $$( - 6 , - 4 ) , ( 3,5 ) , ( - 2,1 )$$ are the vertices of a parallelogram, then remaining vertex can be:

A
$$( 0 , - 1 )$$

B
$$( 7,10 )$$

C
$$( - 1,0 )$$

D
$$( - 11 , - 8 )$$

Solution
Question 4
1 / -0

The distance of the point (1,3) from the line 2x-3y+9=0 measured along a line x-y+1=0 is

A
$$\sqrt 2$$

B
$$\sqrt 5$$

C
$$2\sqrt 2$$

D
1

Solution

Slope of line $$2x-3y+9=0$$ is $$m_1=\frac{2}{3}$$
Slope of line $$x-y+1=0$$ is $$m_2=1$$
Now, angle between the two lines is
$$tan\theta=\frac{m_2-m_1}{1+m_1m_2}=\frac{1-\frac{2}{3}}{1+1\times\frac{2}{3}}=\frac{\frac{1}{3}}{\frac{5}{3}}=\frac{1}{5}$$
So, $$sin\theta=\frac{1}{\sqrt{26}}$$
Now, Perpendicular distance of $$(1,3)$$ from $$2x-3y+9=0$$ is
$$p=\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2}}$$
$$=\frac{|2(1)+(-3)(3)+9|}{\sqrt{(2)^2+(-3)^2}}$$
$$=\frac{|2-9+9|}{\sqrt{4+9}}$$
$$=\frac{2}{\sqrt{13}}$$
Now, distance along the given line $$=\frac{p}{sin\theta}=\frac{2}{\sqrt{13}}\times\sqrt{26}=2\sqrt{2}$$ units
So, the correct option is $$\text{C}$$.
Question 5
1 / -0

If $$L_1$$ is the line of intersection of the plane $$2x-2y+3z-2=0, x-y+z+1=0$$ and $$L_2$$ is the line of intersection of the plane $$x+2y-z-3=0, 3x-y+2z-1=0$$, then the distance of origin from from the plane containing the lines $$L_1$$ + $$L_2$$ is :

A
$$\dfrac{1}{\sqrt{2}}$$

B
$$\dfrac{1}{4\sqrt{2}}$$

C
$$\dfrac{1}{2\sqrt{2}}$$

D
none of these

Solution
Question 6
1 / -0

Which one of the following 3D shapes does not have a vertex?

A
Sphere

B
Pyramid

C
Prism

D
Cone

Solution

The sphere has a round shape and does not form any vertex. But pyramid,prism and cone have atleast one vertex .
So, the answer is option (a) sphere
Question 7
1 / -0

is a point on the line segment joining the points A(2,-3,4) and B(8,0,10). if the value of y-coordinate of C is-2, then the z-coordinate of c is ___________________.

A
4

B
6

C
-4

D
5

Solution
Question 8
1 / -0

Find the ratio on which the plane 3x + 4y - 5z = 1 divides the line joining the points (-2, 4, -6) and (3, -5, 8).

A
3 : 4

B
3 : 5

C
4 : 3

D
2 : 3

Solution
Question 9
1 / -0

The centroid of triangle $$A(3,4,5);B(6,7,2);C(0,-5,2)$$ is

A
$$(3,2,3)$$

B
$$(5,2,1)$$

C
$$(2,5,1)$$

D
$$(3,4,1)$$

Solution

Given points $$A(3,4,5);B(6,7,2);C(0,-5,2)$$
Centroid is given as $$\left(\dfrac{3+6+0}{3},\dfrac {4+7-5}3,\dfrac {5+2+2}{3}\right)\\\left(\dfrac 9 3,\dfrac 63 ,\dfrac 93\right)=(3,2,3)$$
Question 10
1 / -0

The shortest distances of a point from x-axis, y-axis and z-axis are 2,3,6 respectively. The distance of this point from the origin is

A
$$\frac{7}{\sqrt{2}}$$

B
7

C
11

D
$$\frac{49}{2}$$

Solution