Three Dimensional Geometry Test

Result

Three Dimensional Geometry Test - 62

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Question 1
1 / -0

A line segement PQ has the length "63" and dr" s ( 3-2,6 } if the line makes angle with x- axis then components of vector PQ are

A
-24,18,-54

B
-27, 18 , 54

C
7, 8, +-4

D
-7 , 8 , -4

Solution
Question 2
1 / -0

The equation of the plane passing through $$(1, 1, 1)$$ and $$(1, -1, -1)$$ and perpendicular to $$2x - y + z + 5 = 0$$ is

A
$$2x + 5y + z - 8 = 0$$

B
$$x + y - z - 1 = 0$$

C
$$2x + 5y + z + 4 = 0$$

D
$$x - y + z - 1 = 0$$

Solution
Question 3
1 / -0

The direction ratios of two lines are $$(4,3,5)$$ and $$(\lambda, -1, 2)$$. If the angle between them is $$45^{o}$$, a value of $$\lambda$$ is

A
$$0$$

B
$$2$$

C
$$3$$

D
$$-1$$

Solution
Question 4
1 / -0

The st lines whose direction cosines satisfy:
$$al+bm+cn=0$$ and $$fmn+gnl+hlm=0$$ are perpendicular if:

A
$$\dfrac {f}{a}+\dfrac {g}{b}+\dfrac {h}{c}=0$$

B
$$\dfrac {a^{2}}{f}+\dfrac {b^{2}}{g}+\dfrac {c^{2}}{h}=0$$

C
$$\sqrt {af}+\sqrt {bg}+\sqrt {ch}=0$$

D
$$a^{2}f+b^{2}g+c^{2}h=0$$.

Solution
Question 5
1 / -0

If $$l_1$$, $$m_1$$, $$n_1$$ and $$l_2$$, $$m_2$$, $$n_2$$ are the direction cosines of two perpendicular lines, then the direction cosine of the line which is perpendicular to both the lines , will be

A
($$m_1$$$$n_2$$ - $$m_2$$$$n_1$$), ($$n_1$$$$l_2$$ - $$n_2$$$$l_1$$), ($$l_1$$$$m_2$$ - $$l_2$$$$m_1$$)

B
($$l_1$$$$l_2$$ - $$m_1$$$$m_2$$), ($$m_1$$$$m_2$$ - $$n_1$$$$n_2$$), ($$n_1$$$$n_2$$ - $$l_1$$$$l_2$$)

C
$$\dfrac{1} {\sqrt {l^{2}_1+m^{2}_1+n^{2}_1}}$$, $$\dfrac{1} {\sqrt {l^{2}_2+m^{2}_2+n^{2}_2}}$$, $$\dfrac{1} {\sqrt3}$$

D
$$\dfrac{1} {\sqrt3}$$, $$\dfrac{1} {\sqrt3}$$, $$\dfrac{1} {\sqrt3}$$

Solution
Question 6
1 / -0

If two straight lines having directions cosines $$\lambda, m, n$$ and $$f, g, h$$ satisfy $$\lambda+m+n=0$$ and $$fmn+gn\lambda+h\lambda m=0$$ and are perpendicular then $$f+g+h$$ is equal to

A
$$0$$

B
$$1$$

C
$$-1$$

D
$$2$$
Question 7
1 / -0

The Dr's of two lines are 1, -2, -2 and 0, 2, 1 the Dc's of the line perpendicular to the above lines are :-

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

B
$$-\frac { 1 }{ 3 } ,\frac { 2 }{ 3 } ,\frac { 2 }{ 3 } $$

C
$$\frac { 1 }{ 14 } ,\frac { 3 }{ 4 } ,\frac { 2 }{ 3 }$$

D
None of these

Solution
Question 8
1 / -0

In a plane there are 10 points, no three are in same straight line except 4 points which are collinear, then the number of straight lines are

A
39

B
41

C
45

D
40

Solution
Question 9
1 / -0

The point collinder with (1,-2,-3) and (2,0,0) amoung the following is

A
(0,4,6)

B
(0, -4, -5)

C
(0, -4, -6)

D
non of these

Solution
Question 10
1 / -0

A line with direction ratio 2,7,-5 is drawn to intersect the lines $$\frac { x-y }{ 3 } =\frac { y-7 }{ -1 } =\frac { z+2 }{ 1 } $$ and $$\frac { x+3 }{ -3 } =\frac { y-3 }{ 2 } =\frac { z-6 }{ 4 } $$ at P and Q respectively, then length of PQ is-

A
$$\sqrt { 78 } $$

B
$$\sqrt { 77 } $$

C
$$\sqrt { 54 } $$

D
$$\sqrt { 74 } $$

Solution