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This mock test of Mathematics Test 7 - 3-D Vector, Continuity for JEE helps you for every JEE entrance exam.
This contains 30 Multiple Choice Questions for JEE Mathematics Test 7 - 3-D Vector, Continuity (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The points R and S divide PQ internally and externally in the ratio 2:3 respectively. Ifand

are perpendicular, then

Solution:

QUESTION: 2

If the scalar product of the vector i+j+k with a unit

vector parallel to the sum of vectors 2i+4j–5k and

is equal to one, the is equal to

Solution:

QUESTION: 3

Solution:

QUESTION: 4

If A = 2i+2j+3k, B = â€“i+ 2j+ k and C = 3i+ j, then A +t B is perpendicular to C if t is equal to

Solution:

QUESTION: 5

If the vectors a,b and c form the side BC,CA and AB respectively, of a triangle ABC, then

Solution:

QUESTION: 6

Let the vectors a,b,c and d be such that (aÃ—b)Ã—(cÃ—d) =0. Let P1 and P2 be planes determined by the pairs ofvectors a,b and c,d respectively. Then the angle between P1 and P2 is

Solution:

QUESTION: 7

If x and y are two unit vectors and is the angle between them, then is equal to

Solution:

QUESTION: 8

If a and b are two unit vectors such that a+2b and5a–4b are perpendicular to each other, then the angle between a and b is

Solution:

QUESTION: 9

Let a and b be two non-collinear unit vectors. if u = a–(a.b) b and v = a×b, then |v| is

Solution:

QUESTION: 10

If a.b and c are three non-coplanar vecotrs, then (a b c).[(a b)×(a c)] equals

Solution:

QUESTION: 11

If a, b and c are unit coplanar vectors, then the scalar triple product [2a–b 2b–c 2c–a] =

Solution:

QUESTION: 12

If a,b,c be three non-coplanar vectors, then i. [a+b,b+c,c+a] =, ii. [aâ€“b,bâ€“c,câ€“a] =

iii. [aÃ—b,bÃ—c,cÃ—a] =

iii. [aÃ—b,bÃ—c,cÃ—a] =

Solution:

QUESTION: 13

If a,b,c are non-coplanar unit vectors usch that a (b and c non-coplanar) then the

angle between a and b is

angle between a and b is

Solution:

QUESTION: 14

If u = i×(a×i) j×(a×j) k×(a×b), then

Solution:

QUESTION: 15

Let a, b and c be three vectors with magnitudes 1, 1 and 2 respectively. If ax(axc) + b = 0, then the acute angle between a and c is?

Solution:

QUESTION: 16

The directional cosines of the line which is perpendicular to the lines with direction cosines

proportional to 6,4,â€“4 and â€“6,2,1 is

proportional to 6,4,â€“4 and â€“6,2,1 is

Solution:

QUESTION: 17

Angle between the lines whose direction cosine is

given by l m n=0=l2 m2â€“n2 is

given by l m n=0=l2 m2â€“n2 is

Solution:

QUESTION: 18

The lines whose direction cosine are given by the relations a2l b2m c2n = 0 and mn nl lm = 0 are parallel if

Solution:

QUESTION: 19

The point of intersection of the line drawn form thevertices of any tetrahedran to the centroid of opposite faces divide the distance from each vertex to the opposite face in ratio

Solution:

QUESTION: 20

If vertices of tetrahedron are (1,2,3), (2,3,5),(3,â€“1,2) and (2,1,4) then its centroid is

Solution:

QUESTION: 21

If P,Q,A,B are (1,2,5),(â€“2,1,3),(4,4,2) and (2,1,â€“4) then the projection of PQ on AB is

Solution:

QUESTION: 22

Let the coordinates of A,B,C are (1,8,4),(0,â€“11,4), (2,â€“3,1) respectively. The coordinate of a point D

which is foot of the perpendicular from A on BC is

which is foot of the perpendicular from A on BC is

Solution:

QUESTION: 23

The coordinates of A,B,C are A (â€“1,2,â€“3), B(5,0,â€“6), C(0,4,â€“1). The direction cosines of the internal beisector of angle BAC are proportional to

Solution:

QUESTION: 24

Three line with direction ratios 1,1,2; ,4 and , 4 make

Solution:

QUESTION: 25

If acute angle between the planes 2x+ky+z = 6 and x+y+2z = 3 id ,then k equals

Solution:

QUESTION: 26

Equation of the plane passing through the points (0,0,1),(1,0,1) and (1,â€“1,0) is

Solution:

QUESTION: 27

Equation of the plane through the point (4,5,1) and its normal is the line joning the points (3,4,2) and (1,1,1) is

Solution:

QUESTION: 28

If y = then

Solution:

QUESTION: 29

Number of points where f(x) = is not differentiable is

Solution:

QUESTION: 30

The set of points where f(x) is not differentiable is

Solution:

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