12%20-%20Three%20Dimensional%20Geometry

12%20-%20Three%20Dimensional%20Geometry - 12 - THREE...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
12 - THREE DIMENSIONAL GEOMETRY Page 1 ( Answers at the end of all questions ) ( 1 ) If the angle θ between the line 1 1 x + = 2 1 y - = 2 2 z - and the plane 2x - y + x λ + 4 = 0 is such that sin θ = 3 1 , then the value of λ is ( a ) 3 5 ( b ) - 5 3 ( c ) 4 3 ( d ) - 3 4 [ AIEEE 2005 ] ( 2 ) If the plane 2ax - 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres x 2 + y 2 + z 2 + 6x - 8y - 2z = 13 and x 2 + y 2 + z 2 - 10x + 4y - 2z = 8, then a equals ( a ) - 1 ( b ) 1 ( c ) - 2 ( d ) 2 [ AIEEE 2005 ] ( 3 ) The distance between the line r = 2 ^ i - 2 ^ j + 3 ^ k + λ ( ^ i - ^ j + 4 ^ k ) and the plane r . ( ^ i + 5 ^ j + ^ k ) = 5 is ( a ) 9 10 ( b ) 3 3 10 ( c ) 10 3 ( d ) 3 10 [ AIEEE 2005 ] ( 4 ) The angle between the lines 2x = 3y = - z and 6x = - y = - 4z is ( a ) 0 ° ( b ) 90 ° ( c ) 45 ° ( d ) 30 ° [ AIEEE 2005 ] ( 5 ) The plane x + 2y - z = 4 cuts the sphere x 2 + y 2 + z 2 - x + z - 2 = 0 in a circle of radius ( a ) 3 ( b ) 1 ( c ) 2 ( d ) 2 [ AIEEE 2005 ] ( 6 ) A line makes the same angle θ with each of the X- and Z- axis. If the angle β, which it makes with the y-axis, is such that sin 2 β = 3 sin 2 θ , then cos 2 θ equals ( a ) 3 2 ( b ) 5 1 ( c ) 5 3 ( d ) 5 2 [ AIEEE 2004 ]
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
12 - THREE DIMENSIONAL GEOMETRY Page 2 ( Answers at the end of all questions ) ( 7 ) Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is ( a ) 2 3 ( b ) 2 5 ( c ) 2 7 ( d ) 2 9 [ AIEEE 2004 ] ( 8 ) A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The coordinates of each of the points of intersection are given by ( a ) ( 3a, 3a, 3a ), ( a, a, a ) ( b ) ( 3a, 2a, 3a ), ( a, a, a ) ( c ) ( 3a, 2a, 3a ), ( a, a, 2a ) ( d ) ( 2a, 3a, 3a ), ( 2a, a, a ) [ AIEEE 2004 ] ( 9 ) If the straight lines x = 1 + s, y = - 3 - λ s, z = 1 + λ s and x = 2 t , y = 1 + t, z = 2 - t, with parameters s and t respectively, are co-planar, then λ equals ( a ) - 2 ( b ) - 1 ( c ) 2 1 - ( d ) 0 [ AIEEE 2004 ] ( 10 ) The intersection of the spheres x 2 + y 2 + z 2 + 7x - 2y - z = 13
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

12%20-%20Three%20Dimensional%20Geometry - 12 - THREE...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online