Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - JEE MCQ

 are vectors show that   and 

thus what will be the value of   given that 

If the vectors  are such that   form a right handed system then 

 and   are two vectors and   a vector such that

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

Let  is a unit vector such that  is equal to

A particle acted on by constant forces   and   is displaced from the point   to the point  The total work done by the forces is

The vectors  are the sides of a triangle ABC. The length of the median through A is

The shortest distance from the plane 12x + 4 y + 3z = 327 to the sphere x² + y² + z² + 4x - 2y - 6z = 155 is

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

The lines  arecoplanar if

 are 3 vectors, such that  ,  then   is equal to

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

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

and vectrs (1, a,a²),(1, b, b²) and (1, c,c²) are non- coplanar, then the product abc equals

Consider points A , B , C and D with position vectors   and respectively. Then ABCD is a

If  are three non - coplanar vectors, then  equals

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

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y +4z + 5 = 0 is

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

If the straight lines

with parameters s and t respectively, are co-planar, then λ equals.

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

 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

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

If    are non-coplanar vectors and l is a real number, then the vectors    are non coplanar for

 be such that   If the projection   is equal to that of    and   are perpendicular to each other then