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1.

Length of perpendicular from the point `(3,2,1)` to the line `(x-7)/2 = (y-7)/(-2) = (z - 6)/(-3)` isA. `sqrt(46)`B. `sqrt(47)`C. `sqrt(48)`D. `sqrt(49)`

Answer» Correct Answer - D
Discussion
2.

Equation of the plane containing the line ` L_(1) : (x-1)/3 = (y+6)/4 = (z+1)/2 ` , parallel to the line `L_(2) : (x-2)/2 = (y-1)/(-3)= (z+4)/5` , is `26 x - 11y - 17 z ` = p where : p =A. 109B. 110C. 111D. 112

Answer» Correct Answer - A
Discussion
3.

Line ` (x-2)/(-2) = (y+1)/(-3) = (z-5)/1 ` intersects the plane `3x+4y+z = 3 ` in the pointA. `(23/7,29/7,38/7)`B. `(29/7,38/7,23/7)`C. `(38/7,29/7,23/7)`D. `(1,2,8)`

Answer» Correct Answer - C
Discussion
4.

If the line `(x-4)/(1)=(y-2)/(1)=(z-k)/(2)` lies exactly on the plane `2x-4y+z=7`, the value of k isA. 7B. `-7`C. no real valuesD. 4

Answer» Correct Answer - A
Discussion
5.

Distance from the point `(-3,2,5)` to the point where the line `(x+3)/2= (y-2)/2=(z-5)/2` meets the plane `x+y +2z = 3` isA. `7/18`B. `8/17`C. `17/8`D. `18/7`

Answer» Correct Answer - D
Discussion
6.

Distance of the points of intersection of the line `(x-3)/(1)=(y-4)/(2)=(z-5)/(2)and` plane `x+y+z=2` from the point (3,4,5) is

Answer» Correct Answer - B
Discussion
7.

The point at which the line joining the points `(2, -3, 1) and (3, -4, -5)` intersects the plane `2x+y+z=7` isA. `(1,2,-7)`B. `(1,-2,7)`C. `(-1,2,7)`D. `(1,2,7)`

Answer» Correct Answer - B
Discussion
8.

Line `(x-1)/2= (y-2)/3=(z-3)/4` intersects the plane `3x+6y+5z = 0 ` in the point A . Then the direction ratios of the line OA areA. `1,6,-8`B. `8,6,-1`C. `6,8,1`D. `8,1,-6`

Answer» Correct Answer - D
Discussion
9.

Distance of the point of intersection of the line `(x-2)/3=(y+1)/4=(z-2)/12` and the plane `x-y+z = 5 ` from the point `(-1,-5,-10)` is

Answer» Correct Answer - D
Discussion
10.

Equations of the line joining `(2,-3,1)and (3,-4,-5)` areA. `(x-2)/3 =(y+3)/(-4) = (z-1)/(-5)`B. `(x-3)/2=(y+4)/(-3) (z+5)/1`C. `2-x = y +3 = (z-1)/6`D. `(x-2)/3 = (y+4)/(-3) = (z-1)/(-1)`

Answer» Correct Answer - C
Discussion
11.

Find the equation of the plane which contains two parallel to lines `(x-4)/1=(y-3)/(-4)=(z-2)/5 a n d (x-3)/1=(y+2)/(-4)=z/5dot`A. `11x-y -3z =35`B. `11x-y+3z=35`C. `11x+y-3z=35`D. `11x+y+3z=53`

Answer» Correct Answer - A
Discussion
12.

Equations of the line through `(4,-5,6)` and perpendicular to the lines `(x-11)/1=(y+6)/(-3) = (z-5)/0 `and `(x-1)/5 = (y-2)/2=(z-8)/11` areA. `(x-1)/3 = (y-2)/2 = (z-8)/11 `B. `(x-4)/(-33) = (y+5)/(-11)=(z-6)/7`C. `(x-4)/3 = (y+5)/1 = (y-6)/(-17)`D. `3(x-4)-3 (y+5)+11(z-6)=0`

Answer» Correct Answer - A
Discussion
13.

Equations of the line passing through the origin and the point (a,b,c) areA. ` (x-a)/(x-0) = (y-b)/(y-0)=(z-c)/(z-0)`B. `(x-a)/a=(y-b)/b=(z-c)/c`C. `(x-a)/(b-c)=(y-b)/(c-a)=(z-c)/(a-b)`D. `a(x-a)=b(y-b)=c(z-c)`

Answer» Correct Answer - B
Discussion
14.

Distance of the point `(1,-2,3)` from the plane `x-y+z = 5` measured parallel to the line whose direction cosines are proportional to `2,3,-6` isA. 1B. 2C. 3D. 4

Answer» Correct Answer - A
Discussion
15.

The line `(x-2)/3 = (y-3)/4 = (z-4)/5` is parallel to the planeA. `3x+4y+5z=8`B. `2x+3y+4=0`C. `x+y-z=2`D. `2x+y-2z=0`

Answer» Correct Answer - D
Discussion
16.

Equations of the line passing through `(1,2,3)and (-3,4,3)` areA. ` (x-1)/(-4) = (y-2)/(-2) = (z-3)/0`B. `(x-1)/(-4)= (y-2)/(-2)`C. `(x-1)/2 = 2- y = (z-3)/0`D. ` (x -2)/(-3) = (y-4)/2 = (z-3)/3 `

Answer» Correct Answer - C
Discussion
17.

Equations of the line passing through (a,b,c) and parallel to Z - axis , areA. `x-a = y-b = z `B. `(x-a)/0 = (y-b)/0=(z-c)/1`C. `(x-a)/1 = (y-b)/1 = (z-c)/0`D. `x-a = y - b = z - c`

Answer» Correct Answer - B
Discussion
18.

Equations of the line passing through (a,b,c) and perpendicular to Z - axis areA. `(x-a)/l = (y-b)/m = (z-c)/0`B. `(x-a)/0 = (y-b)/0 = (z-c)/(abc)`C. `(x-a)/a = (y-b)/b = z `D. `(x-l)/a = (y-m)/b = (z - n)/c`

Answer» Correct Answer - A
Discussion
19.

Find ten equation of the plane passing through the point `(0,7,-7)`and containing the line `(x+1)/(-3)=(y-3)/2=(z+2)/1`.A. `-3x+2y+z=0`B. `y+z=0`C. `x+y+z=0`D. `x+2y+z=7`

Answer» Correct Answer - C
Discussion
20.

Co - ordinates of the foot of the perpendicular drawn from the origin to the plane `2x+3y-4z + 1 = 0 ` areA. `(-2/29,3/29,4/29)`B. `(2/29,-3/29,4/29)`C. `(-2/29,-3/29,4/29)`D. `(2/29,3/29,-4/29)`

Answer» Correct Answer - C
Discussion
21.

Equations of the line passing through `(-1,2,-3)` and parallel to the line `(x-2)/3 = (y+1)/(-5) = (z+3)/(-7)` areA. `(x-1)/3=(y+2)/(-5)=(z-3)/(-7)`B. `(x+1)/3=(2-y)/5=(z=3)/(-7)`C. `(x+1)/(-3)=(y-2)/(-5)=(z+3)/7`D. `3(x-1)=5(y+1)=-7(z+3)`

Answer» Correct Answer - B
Discussion
22.

Equations of the passing through the point `(0,1,2)` and equally inclined to the co - ordinates axes are ,A. ` x = y +1 = z +2`B. `x/0=y/1=z/2`C. `0/x=1/y=2/z`D. `x=y-1=z-2`

Answer» Correct Answer - D
Discussion