35 Year JEE Previous Questions: Vector Algebra and Three Dimensional Geometry
MCQ Practice Test & Solutions: Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry (82 Questions)
You can prepare effectively for JEE Crack JEE with 35 Years of Previous Year Solved Papers with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry". These 82 questions have been designed by the experts with the latest curriculum of JEE 2026, to help you master the concept.
Test Highlights:
- - Format: Multiple Choice Questions (MCQ)
- - Duration: 160 minutes
- - Number of Questions: 82
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A plane which passes through the point (3, 2, 0) and the line
Detailed Solution: Question 1
and the angle between 
then 
is equal to
and the angle between then is equal toDetailed Solution: Question 2
are vectors such that 
then 
are vectors such that then Detailed Solution: Question 3
are vectors show that 
and 
are vectors show that and Detailed Solution: Question 4
thus what will be the value of 
given that 
thus what will be the value of given that Detailed Solution: Question 5
If the vectors 
are such that 
form a right handed system then 
are such that form a right handed system then Detailed Solution: Question 6
form a right handed system,
and 
are two vectors and 
a vector such that 
and are two vectors and a vector such that Detailed Solution: Question 7
Detailed Solution: Question 8
The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle π /4 with plane x + y = 3 are
Detailed Solution: Question 9
Let 
is a unit vector such that 
is equal to
is a unit vector such that is equal toDetailed Solution: Question 10
perpendicular 
A particle acted on by constant forces 
and 
is displaced from the point 
to the point 
The total work done by the forces is
and is displaced from the point to the point The total work done by the forces isDetailed Solution: Question 11
The vectors 
are the sides of a triangle ABC. The length of the median through A is
are the sides of a triangle ABC. The length of the median through A isDetailed Solution: Question 12
The shortest distance from the plane 12x + 4 y + 3z = 327 to the sphere x2 + y2 + z2 + 4x - 2y - 6z = 155 is
Detailed Solution: Question 13
The two lines x = ay + b , z = cy + d and x = a`y + b`, z = c`y + d` will be perpendicular, if and only if
Detailed Solution: Question 14
The lines 
arecoplanar if
arecoplanar ifDetailed Solution: Question 15
are 3 vectors, such that 
, then 
is equal to
are 3 vectors, such that , then is equal toDetailed Solution: Question 16
The radius of the circle in which the sphere
x2 + y2 + z2 + 2x - 2y - 4z - 19 = 0 is cut by the plane x + 2y + 2z + 7 = 0 is
Detailed Solution: Question 17
A tetrahedron has vertices at O(0, 0, 0), A(1, 2, 1) B(2, 1, 3) and C(–1, 1, 2). Then the angle between the faces OAB and ABC will be
Detailed Solution: Question 18
and vectrs (1, a,a2),(1, b, b2) and (1, c,c2) are non- coplanar, then the product abc equals
and vectrs (1, a,a2),(1, b, b2) and (1, c,c2) are non- coplanar, then the product abc equalsDetailed Solution: Question 19
Consider points A , B , C and D with position vectors 
and 
respectively. Then ABCD is a
and respectively. Then ABCD is aDetailed Solution: Question 20
If 
are three non - coplanar vectors, then 
equals
are three non - coplanar vectors, then equalsDetailed Solution: Question 21
Two system of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a' , b' , c' from the origin then
Detailed Solution: Question 22
Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y +4z + 5 = 0 is
Detailed Solution: Question 23
...(2)
A line with direction cosin es proportional to 2, 1, 2 meets each of the lines x = y + a = z an d x + a = 2y = 2z . The co-ordinates of each of the points of intersection are given by
Detailed Solution: Question 24
then direction ratio of the line joining these poin ts are
If the straight lines
with parameters s and t respectively, are co-planar, then λ equals.
Detailed Solution: Question 25
The intersection of the spheres
x2 + y2 + z2 + 7x - 2y - z = 13 and x2 + y2 + z2 -3x + 3y + 4z = 8
is the same as the intersection of one of the sphere and the plane
Detailed Solution: Question 26
be three non -zero vectors such that no two of these are collinear. If the vector 
is collinear with 
is collinear with 
(λ being some non-zero scalar) then 
equals
be three non -zero vectors such that no two of these are collinear. If the vector is collinear with is collinear with (λ being some non-zero scalar) then equalsDetailed Solution: Question 27
wh ere t and s are scalars. Adding, we get
A particles is acted upon by constant forces 
and 
which displace it from a point 
to the point 
The work done in standard units by the forces is given by
and which displace it from a point to the point The work done in standard units by the forces is given byDetailed Solution: Question 28
If 
are non-coplanar vectors and l is a real number, then the vectors 
are non coplanar for
are non-coplanar vectors and l is a real number, then the vectors are non coplanar forDetailed Solution: Question 29
be such that 
If the projection 
is equal to that of 
and 
are perpendicular to each other then 
be such that If the projection is equal to that of and are perpendicular to each other then Detailed Solution: Question 30
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