Three Dimensional Geometry Test

Result

Three Dimensional Geometry Test - 61

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Question 1
1 / -0

If $$AB=21,\ B\equiv (-2,1,-8)$$ and the direction cosines of $$AB$$ are $$\dfrac{6}{7},\dfrac{2}{7},\dfrac{3}{7}$$ then the coordinates of $$A$$ are

A
$$(-16,-7,-1)$$

B
$$(-20,-5,17)$$

C
$$(16,7,1)$$

D
$$(20,5,17)$$

Solution

$$\begin{array}{l} Let\, \, coordinate\, \, of\, \, A\left( { x,y,z } \right) \\ B\left( { -2,1,-8 } \right) \, \, given \\ \Rightarrow AB=\sqrt { (x+{ 2^{ 2 } }+{ { \left( { y-1 } \right) }^{ 2 } }{ { \left( { z+8 } \right) }^{ 2 } } } \\ \Rightarrow direction\, \, of\, \, AB=\frac { { \left( { x+2 } \right) } }{ { { z_{ 1 } } } } ,\frac { { \left( { y-1 } \right) } }{ { { z_{ 1 } } } } .\frac { { \left( { z+8 } \right) } }{ { { z_{ 1 } } } } \\ \frac { { x+2 } }{ { { z_{ 1 } } } } =\frac { 6 }{ 7 } \\ \therefore x=16 \\ \frac { { y-1 } }{ { { z_{ 1 } } } } =\frac { 2 }{ 7 } \\ \therefore y=7\, \, and\, \, { }\frac { { z+8 } }{ { { z_{ 1 } } } } =\frac { 3 }{ 7 } ,z=1 \\ Hence,\, \, \, coordinate\, \, of\left( { 16,7,1 } \right) \end{array}$$
Question 2
1 / -0

If from the point $$P ( f , g , h )$$ perpendiculars $$PL , PM$$ be drawn to $$y z$$ and $$zx$$ planes then the equation to the plane $$OLM$$ is -

A
$$\frac { x } { f } + \frac { y } { g } + \frac { z } { h } = 0$$

B
$$\frac { x } { f } + \frac { y } { g } - \frac { z } { h } = 0$$

C
$$- \frac { x } { f } + \frac { y } { g } + \frac { z } { h } = 0$$

D
$$\frac { x } { f } - \frac { y } { g } + \frac { z } { h } = 0$$

Solution
Question 3
1 / -0

If the d.c's of two lines are such that $$l+3m+n=0,{ 3l }^{ 2 }+{ 5m }^{ 2 }-{ 4n }^{ 2 }=0$$, then the angle between them is

A
$$\dfrac { \pi }{ 3 } $$

B
$$\dfrac { \pi }{ 2 } $$

C
$$\dfrac { \pi }{ 4 } $$

D
$$\dfrac { \pi }{ 6 } $$
Question 4
1 / -0

If the angle between the lines, $$\dfrac { x }{ 2 } =\dfrac { y }{ 2 } =\dfrac { z }{ 1 } $$ and $$\dfrac { 5-x }{ -2 } =\dfrac { 7y-14 }{ P } =\dfrac { z-3 }{ 4 } $$ is $$\cos { ^{ -1 }\left( \dfrac { 2 }{ 3 } \right) } $$, then p is equal to:

A
$$-\dfrac { 4 }{ 7 } $$

B
$$\dfrac { 7 }{ 2 } $$

C
$$-\dfrac { 7 }{ 4 } $$

D
$$\dfrac { 2 }{ 7 } $$

Solution
Question 5
1 / -0

The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to ( 1, -1,2 ) and ( 2,1,-1) are:-

A
$$\frac { 1 }{ \sqrt { 35 } } ,-\frac { 5 }{ \sqrt { 35 } } ,\frac { 3 }{ \sqrt { 35 } } $$

B
$$-\frac { 1 }{ \sqrt { 35 } } ,\frac { 5 }{ \sqrt { 35 } } ,\frac { 3 }{ \sqrt { 35 } } $$

C
$$\frac { 1 }{ \sqrt { 35 } } ,\frac { 5 }{ \sqrt { 35 } } ,\frac { 3 }{ \sqrt { 35 } } $$

D
none of these

Solution
Question 6
1 / -0

The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to $$(1, -1, 2)$$ and $$(2, 1, -1)$$ are

A
$$\dfrac{-1}{\sqrt{35}}, \dfrac{5}{\sqrt{35}}, \dfrac{3}{\sqrt{35}}$$

B
$$\dfrac{13}{\sqrt{35}}, \dfrac{-1}{\sqrt{35}}, \dfrac{1}{\sqrt{35}}$$

C
$$\dfrac{2}{\sqrt{3}}, \dfrac{5}{\sqrt{3}}, \dfrac{7}{\sqrt{3}}$$

D
$$\dfrac{3}{\sqrt{35}}, \dfrac{5}{\sqrt{35}}, \dfrac{7}{\sqrt{35}}$$

Solution
Question 7
1 / -0

If $$(2,1,3)$$ and $$(-1,2,4)$$ are the extermities of a diagonal of a rhombus then the $$d.r's$$ of the other diagonal are

A
$$(2,3,-9)$$

B
$$(-2,3,-9)$$

C
$$(1,-2,4)$$

D
$$(2,3,1)$$

Solution
Question 8
1 / -0

A mirror and source of light are kept at the origin and the positive x-axis respectively a ray a light from the sources strikes the mirror and is reflected. If (1,-1,1) are the Dr's of a normal to the plane. Then the D.C's of the reflected ray are

A
$$(\frac{-1}{3},\frac{-2}{3},\frac{2}{3})$$

B
$$(\frac{1}{3},\frac{2}{3},\frac{2}{3})$$

C
$$(\frac{1}{3},\frac{-2}{3},\frac{2}{3})$$

D
$$(\frac{-1}{3},\frac{2}{3},\frac{2}{3})$$

Solution
Question 9
1 / -0

If the incident ray and normal have the directions of the vectors $$\left(1,-3,1\right),\left(1,1,1\right)$$ respectively, then direction of the reflected ray is-

A
$$\left(4,-8,4\right)$$

B
$$\left(5,-7,5\right)$$

C
$$\left(6,-6,6\right)$$

D
$$\left(-5,7,5\right)$$

Solution
Question 10
1 / -0

The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to (1,-1,2) and (2,1,-1) are:-

A
$$\frac { 1 }{ \sqrt { 35 } } ,-\frac { 5 }{ \sqrt { 35 } } ,\frac { 3 }{ \sqrt { 35 } } $$

B
$$-\frac { 1 }{ \sqrt { 35 } } ,\frac { 5 }{ \sqrt { 35 } } ,\frac { 3 }{ \sqrt { 35 } } $$

C
$$\frac { 1 }{ \sqrt { 35 } } ,\frac { 5 }{ \sqrt { 35 } } ,\frac { 3 }{ \sqrt { 35 } } $$

D
None of these

Solution