parallel to x-axis
parallel to y-axis
parallel to z-axis
equally inclined to all the axes
`( 0 , -7/2 , 5/2)`
`( 0 , 7/2 , 1/2 )`
`( 0 , -7/2 , -5/2)`
`( 0 , 7/2 , -5/2)`
`ae+cg-1=0`
`ae+ bf -1 = 0`
`ae+cg+1=O`
`ag+ce+ 1 = 0`
`< 2, - 5, 3 >`
`< 1, - 5, - 3 >`
`< 2,5, 3>`
`< 1, 3,5 >`
`2x+5y-2=0`
`5x+ 2y -5=0`
`x + z- 2 = 0`
`2x- y - 2z = 0`
` 2/sqrt(29)`
` 4/sqrt(29)`
` 5/sqrt(29)`
`1`
`(pm (12)/(13) , pm (4)/(13) , pm (3)/(13) )`
`( (12)/(13) , - (4)/(13) , (3)/(13) )`
`( (12)/(13) , - (4)/(13) , - (3)/(13) )`
`(- (12)/(13) , - (4)/(13) , (3)/(13) )`
are perpendicular
are parallel
intersect at an angle `45^0`
intersect at an angle `60^0`
`(1, 6, 4)`
`( -1, 6, -4)`
`(-1, -6, 4)`
`(2, -6, 4)`
`2`
`3`
`4`
`5`
`3, 6, 9`
`1, 2, 3`
`1, 4, 9`
`2, 4, 6`
`< 2,-1,2 >`
`< -2,1,2 >`
`< 2, 1, - 2 >`
`< - 2,- 1,- 2 >`
`x+2y+3z=1`
`3x+2y+z=3`
`2x+3y+6z=18`
`6x+3y+2z=18`
`(0, 5, 4)`
`(3,5, 0)`
`(3,0, 4)`
`(0, 0, 4)`
` sqrt(10) units`
` sqrt(14) units`
`4 units`
`5 units`
`(5, 2, 1)` units
`( (13)/5, ( 13)/2 ,13)` units
`( 5/(13) , 2 /(13) , 1/(13))` units
`(1, 2, 5)` units
`x + y = 3`
`x - y = -1`
`z = 3`
`x+2y+3z=14`
are collinear
form an equilateral triangle
form a scalene triangle
form a right-angled triangle
`(-1, 2,- 3)`
`(1,- 2, 3)`
`(1,2,-3)`
`(-1,-2,-3)`
`(0, - 4, -1)`
`(0, - 4, 1)`
`(1, 4, 0)`
`(0, 4, 1)`
`1 : 1`
`2: 3`
`3 : 4`
None of these
`(1, 0, 0)`
`(1, 0, 1)`
`(0, 0, 1)`
None of these
`< 1,0, 1 >`
` < 0, 1,0 >`
`< 1, 0, -1 >`
None of these
`< 2, 3, - 1 >`
`< 2, 3, 1 >`
`< -1, 2, 3 >`
None of these
`1 /sqrt(3)`
`1/sqrt(2)`
`2/sqrt(6)`
None of these
`30^0`
`60^0`
`90^0`
`120^0`
`< 1/2 , sqrt(3)/2 , 0 >`
`< 1/2 , - sqrt(3)/2 , 0 >`
`< 1/sqrt(2) , 1/sqrt(2) , 0 >`
`< -1/2 , sqrt(3)/2 , 0 >`
`< 4, - 4, 2 >`
`< 4, 4, 2 >`
`< -4, 4, 2 >`
`< 2, 1, 1 >`
`theta = 30^(circ)`
`theta = 45^(circ)`
`2 cos theta =1`
`3 cos theta =1`
`x^2 + y^2 + z^2 = 0`
`x^2 + y^2 + z^2 = 1`
`x^2 + y^2 + z^2 = 2`
`x^2 + y^2 + z^2 = 3`
`0`
`1/3`
`1`
`3`
`1` unit
`1.5` units
`2` units
`2.5` units
`0`
`1/3`
`1`
`3`
`3 sqrt(5)` sq units
`6 sqrt(5)`sq units
`6` sq units
`12` sq units
3 units
1 unit
0
None of these
`1/4`
`1/2`
`3/4`
`1`
`3`
`2`
`1`
`-1`
`pi/6`
`pi/4`
`pi/3`
`pi/2`
`I + m + n = 0`
`a + b + c = 0`
`a/l + b/m +c/n =0`
`al + bm + cn = 0`
1 unit
2 units
3 units
4 units
`(r cos alpha , 0, r sin alpha)`
`(0, 0, r sin alpha)`
`(r cos alpha , 0, 0)`
`(0, 0, r cos alpha)`
` (: 1/sqrt(3) , 1/sqrt(3) , 1/sqrt(3) :)`
` (: - 1/sqrt(3) , 1/sqrt(3) , 1/sqrt(3) :)`
` (: - 1/sqrt(3) , - 1/sqrt(3) , 1/sqrt(3) :)`
` (: 1/3 , 1/3 , 1/3 :)`
`pi/2`
`pi/3`
`pi/6`
None of these
`3x + 4y + 5z + 4 = 0`
`3x + 4y- 5z + 14 = 0`
`3x + 4y -· 5z + 4 = 0`
`3x + 4y- 5z- 4 = 0`
`(: 1,2,3 :)`
`(: 2,1,3 :)`
`(: 3,2,1 :)`
`(: 1,3,2 :)`
`(x-a)/1 = (y-b)/0 = (z-c)/0`
`(x-a)/0 = (y-b)/0 = (z-c)/1`
`(x-a)/0 = (y-b)/1 = (z-c)/0`
`(x-a)/0 = (y-b)/1 = (z-c)/1`
`1/2`
`1/3`
`2/3`
None of these
`0`
`1`
`3`
`2/(sqrt (26))`
4 units
5 units
6 units
12 units
`-1`
`0`
`1`
`2`
`pi/5`
`pi/4`
`pi/6`
`pi/3`
`sqrt (3/4)`
`sqrt (1/2)`
`sqrt (3/2)`
`1/3`
Only I
Only II
Both I and II
Neither I ror II
`(3, 2, 2)`
`(3, 7, 1)`
`(1, 2. 3)`
`(2, 1, -1)`
`90^(circ)`
`60^(circ)`
`45^(circ)`
`30^(circ)`
one point only in common
three points in common
infinite points in common
no points in common
`1`
`2`
`3`
`6`
`(sqrt (165))/2` sq units
`(sqrt (135))/2` sq units
`4` sq unit
`2` sq unit
`a + b + c = 0`
`a = b = c`
`al+ bm + cn= 0`
`I+ m + n = 0`
`6`
`12`
`15`
More than `15`
`24`
`12`
`6`
`3`
`cos^(-1) (1/2)`
`cos^(-1) (1/3)`
`cos^(-1) (1/sqrt(3))`
`cos^(-1) (2/sqrt(3))`
`cos^(-1) (1/2)`
`cos^(-1) (1/3)`
`cos^(-1) (1/sqrt(3))`
`cos^(-1) (2/sqrt(3))`
`cos^(-1) (1/sqrt(3))`
`cos^(-1) (2/sqrt(3))`
`cos^(-1) (sqrt(2/3))`
`cos^(-1) (sqrt(2)/3)`
`x cot theta + y = 0`
`x tan theta - y = 0`
`x + y cot theta = 0`
`x-y tan theta = 0`
`-1`
`1`
`-3`
`3`
`sqrt(3)`
`sqrt(6)`
`3`
None of these
`sqrt(3)`
`2`
`2 sqrt(2)`
`4`
`1`
`3`
`sqrt (11)`
`11`
`pi/4`
`pi/6`
`pi/3`
`pi/2`
`x^2 + y^2 + z^2 + 12x- 2y + 4z + 16 =0`
`x^2 + y^2 + z^2 + 12x - 2 y + 4z - 16 = 0`
`x^2 + y^2 + z^2 - 12x + 2y- 4z + 16 = 0`
`x^2 + y^2 + z^2 - 12x + 2y- 4z + 25 = 0`
`(-1, 3,2)`
`(-1,-3,2)`
`(2, 1, 3)`
`(2, 3,2)`
`cos^(-1) (1/5)`
`cos^(-1) (1/7)`
`sin^(-1) (1/5)`
`sin^(-1) (1/7)`
`u^2 + v^2 + w^2 = d^2`
`u^2 + v^2 + w^2 > d`
`u^2 + v^2 + w^2 < d`
`u^2 + v^2 + w^2 < d^2`
`pi/2`
`pi/3`
`pi/4`
`pi/6`
`x + y + z = 6`
`x=1`
` y+z =5`
`z+y =1`
`3`
`2`
`1`
`0`
`(1, 2, 3)`
`(2, 3, 1)`
`(3, 1, 2)`
`(1,3,2)`
`cos^(-1) (1/sqrt(2) )`
`cos^(-1) (1/sqrt(3) )`
`cos^(-1) (1/3 )`
`cos^(-1) (1/2 )`
`0`
`1`
`2`
`3`
`X`-axis
`Y`-axis
`Z`-axis
None of these
`x+ 2y + z = 6`
`x- 2y + z = 6`
`x + 2y- z = 6`
`x- 2y- z = 6`
`49`
`7`
`-49`
`-7`
an ellipse
a circle
a parabola
None of these
`alpha = beta = gamma =1`
`alpha = beta = gamma = 3/7`
`alpha = beta = gamma`
None of these
`4x + 3y- 5z = 0`
`4x + 5y- 4z = 0`
`4x + 4y- 5z = 0`
`5x + 4y- 5z = 0`
`theta < 30^(circ)`
`theta = 60^(circ)`
` 30^(circ) < theta < 60^(circ)`
`theta > 60^(circ)`
`x- z = 0`
`z + y = ()`
`3x + 2y = 0`
`3x + 2z = 0`
`alpha alpha' + beta beta' +1 =0`
`(alpha + alpha ') (beta + beta') =0`
`ll'+mm'+n n'= 1`
`ll'+mm'+n n' =0`
`5 :4`
`3:4`
`1:2`
`7:5`
Only I
Only II
Only Ill
Both II and1111
`ax + by+ cz = ax_1 + by_1 + cz_1`
`a(x + x_1)+ b(y+ y_1)+ c(z+ z_1)= 0`
`ax + by+ cz = 0`
`ax+ by+ cz = x_1 + y_1 + z_1 = 0`
`(-1, -7, 5)`
`(-1, 7, 5)`
`(-1/sqrt(75) , - 7/(sqrt(75) ) , 5/(sqrt(75)))`
`(-1/sqrt(75) , 7/(sqrt(75) ) , 5/(sqrt(75)))`
`(-3,- 4,- 5)`
`(3, 4, 5)`
`(3, 4, - 5)`
`(-3, 4,- 5)`
`1`
`3`
`3xyz`
`27xyz`
`x^2 + a^2 = 2c^2 - y^2- z^2`
`x^2 + a^2 = c^2 - y^2 - z^2`
` x^2 - a^2 = c^2 - y^2 - z^2`
`x^2 + a^2 = c^2 + y^2 + z^2`
at a point
at two points
at three points
in a line
Assertion : If `(: l, m, n :)` are directiod cosines of a line, there can be a line whose direction cosines are `(: sqrt ((l^2+m^2)/2) , sqrt((m^2+n^2)/2) , sqrt((n^2 +l^2)/2) :)`
Reason : The sum of direction cosines of a line is unity.
`2x- 3y = 0`
`5x- 2z = 0`
`5y- 3z = 0`
`3x -2y= 0`