Introduction to Three Dimensional Geometry Test

Result

Introduction to Three Dimensional Geometry Test - 39

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Question 1
1 / -0

If A = (2,-3,1), B = (3,-4,6) and C is a point of trisection of AB, then $${ C }_{ y }$$

A
$$\frac { 11 }{ 3 } $$

B
-11

C
$$\frac { 10 }{ 3 } $$

D
$$\frac { -11 }{ 3 } $$

Solution
Question 2
1 / -0

The coordinates of the orthocentre of the triangle that has the coordinates of mid points of its sides as (0 , 0) (1 , 2) and ( -6 , 3) is :

A
(0 , 0)

B
(-4 , 5)

C
(-5 , 5)

D
(-4 , 4)
Question 3
1 / -0

Let $$A(2,3,5),B(-1,3,2)$$ and $$C(\lambda ,5,\mu )$$ are the vertices of a triangle and its median through A meets side BC at D. AD is equally inclined with the axes. If E is the point on BC such that $$BE:EC=1:2.$$
Equation of plane containing triangle ABC

A
$$x+y+3=0$$

B
$$x-z-3=0$$

C
$$x-z+3=0$$

D
$$x-y+3=0$$
Question 4
1 / -0

Consider a variable plane $$lx+my+nz=k(k>0)and\quad l,m,n$$ are direction cosines of normal of the plane. Let the given plane intersects the co-ordinate axes at A,B and C, then the minimum area of $$\triangle ABC$$ is _______.

A
$$\dfrac { 3\sqrt { 3k } ^{ 2 } }{ 2 } $$

B
$$\dfrac { 3\sqrt { 3k } ^{ 2 } }{ 4 } $$

C
$$3\sqrt { 3 } { k }^{ 2 }$$

D
$$12\sqrt { 3 } { k }^{ 2 }$$

Solution
Question 5
1 / -0

The shortest distance between the point $$\left( \dfrac { 3 }{ 2 } ,0 \right) $$ and the curve $$y=\sqrt { x } $$, $$(x>0)$$, is:

A
$$\dfrac { 3 }{ 2 } $$

B
$$\dfrac { \sqrt { 3 } }{ 2 } $$

C
$$\dfrac { \sqrt { 5 } }{ 2 } $$

D
$$\dfrac { 5 }{ 4 } $$

Solution
Question 6
1 / -0

If $$A=(1, 2, 3)$$ and $$B(3, 5, 7)$$ and P, Q are the points on AB such that AP$$=$$PQ$$\neq$$QB, then the mid point of PQ is?

A
$$(2, 3, 5)$$

B
$$\left(2, \dfrac{7}{2}, 5\right)$$

C
$$(2, 4, 5)$$

D
$$(4, 7, 0)$$

Solution
Question 7
1 / -0

If $$A=(1, -2, -1), B=(4, 0, -3); C=(1, 2, -1)$$ and $$D=(2, -4, -5)$$, then the distance between AB and CD is?

A
$$\dfrac{2}{3}$$

B
$$\dfrac{4}{3}$$

C
$$\dfrac{3}{2}$$

D
$$\dfrac{5}{3}$$

Solution
Question 8
1 / -0

The equation of plane which is passing through the point $$(1,2,3)$$ and which is at maximum distance from the point $$(-1,0,2)$$ is

A
$$2x+2y+z=9$$

B
$$2x+z=5$$

C
$$3x+y-z=2$$

D
none of these

Solution
Question 9
1 / -0

The distance of the point $$(2,1,-1)$$ from the line $$\dfrac{x-1}{2}=\dfrac{y+1}{1}=\dfrac{z-3}{-3}$$ measured parallel to the plane $$x+2y+z=4$$ is

A
$$\sqrt{10}$$

B
$$\sqrt{20}$$

C
$$\sqrt{5}$$

D
$$\sqrt{30}$$

Solution
Question 10
1 / -0

A line passes through two points A(2, -3, -1) and B(8, -1, 2) the coordinates of a point on this line nearer to the origin at a distance of 14 units from A are

A
(14 , 1, 5)

B
(-10, -7, -7)

C
(10 , 7, 7)

D
(-14, -1, -5)

Solution