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Mathematics Test 7 - 3-D Vector, Continuity


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25 Questions MCQ Test JEE Main & Advanced Mock Test Series | Mathematics Test 7 - 3-D Vector, Continuity

Mathematics Test 7 - 3-D Vector, Continuity for JEE 2022 is part of JEE Main & Advanced Mock Test Series preparation. The Mathematics Test 7 - 3-D Vector, Continuity questions and answers have been prepared according to the JEE exam syllabus.The Mathematics Test 7 - 3-D Vector, Continuity MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Mathematics Test 7 - 3-D Vector, Continuity below.
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Mathematics Test 7 - 3-D Vector, Continuity - Question 1

Let p and q be the position vectors of P and Qrespectively, with respect to O and |p| =p, |q| = q.
The points R and S divide PQ internally and externally in the ratio 2:3 respectively. Ifand
are perpendicular, then

Detailed Solution for Mathematics Test 7 - 3-D Vector, Continuity - Question 1
Mathematics Test 7 - 3-D Vector, Continuity - 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

Mathematics Test 7 - 3-D Vector, Continuity - Question 3

The unit vectors perpendicular to vectors i–j and i+j forming a right handed system is

Mathematics Test 7 - 3-D Vector, Continuity - Question 4
If A = 2i+2j+3k, B = –i+ 2j+ k and C = 3i+ j, then A +t B is perpendicular to C if t is equal to
Mathematics Test 7 - 3-D Vector, Continuity - Question 5
If the vectors a,b and c form the side BC,CA and AB respectively, of a triangle ABC, then
Mathematics Test 7 - 3-D Vector, Continuity - Question 6
Let the vectors a,b,c and d be such that (a×b)×(c×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
Mathematics Test 7 - 3-D Vector, Continuity - Question 7
If x and y are two unit vectors and is the angle between them, then is equal to
Mathematics Test 7 - 3-D Vector, Continuity - 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

Mathematics Test 7 - 3-D Vector, Continuity - 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

Mathematics Test 7 - 3-D Vector, Continuity - Question 10

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

Mathematics Test 7 - 3-D Vector, Continuity - Question 11

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

Mathematics Test 7 - 3-D Vector, Continuity - Question 12
If a,b,c be three non-coplanar vectors, then i. [a+b,b+c,c+a] =, ii. [a–b,b–c,c–a] =
iii. [a×b,b×c,c×a] =
Mathematics Test 7 - 3-D Vector, Continuity - 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
Mathematics Test 7 - 3-D Vector, Continuity - Question 14

If u = i×(a×i) j×(a×j) k×(a×b), then

Mathematics Test 7 - 3-D Vector, Continuity - 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?

Mathematics Test 7 - 3-D Vector, Continuity - Question 16
The directional cosines of the line which is perpendicular to the lines with direction cosines
proportional to 6,4,–4 and –6,2,1 is
Mathematics Test 7 - 3-D Vector, Continuity - Question 17
Angle between the lines whose direction cosine is
given by l m n=0=l2 m2–n2 is
Mathematics Test 7 - 3-D Vector, Continuity - Question 18

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

Mathematics Test 7 - 3-D Vector, Continuity - 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
Mathematics Test 7 - 3-D Vector, Continuity - Question 20
If vertices of tetrahedron are (1,2,3), (2,3,5),(3,–1,2) and (2,1,4) then its centroid is
*Answer can only contain numeric values
Mathematics Test 7 - 3-D Vector, Continuity - Question 21

 are three vectors of which every pair is non collinear. If the vector  and  are collinear with  respectively then  is :-


Detailed Solution for Mathematics Test 7 - 3-D Vector, Continuity - Question 21

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Mathematics Test 7 - 3-D Vector, Continuity - Question 22

Let be vectors such that  is :-


Detailed Solution for Mathematics Test 7 - 3-D Vector, Continuity - Question 22

*Answer can only contain numeric values
Mathematics Test 7 - 3-D Vector, Continuity - Question 23

If then λ + μ is equal to :-


Detailed Solution for Mathematics Test 7 - 3-D Vector, Continuity - Question 23

*Answer can only contain numeric values
Mathematics Test 7 - 3-D Vector, Continuity - Question 24

If a straight line make angles α, β, γ and δ with four diagonals of a cube, then the value of sin2 α + sin2 β + sin2 γ + sin2 δ is –


*Answer can only contain numeric values
Mathematics Test 7 - 3-D Vector, Continuity - Question 25

If the lines  intersect each other, then (λ + m) is equal to –


Detailed Solution for Mathematics Test 7 - 3-D Vector, Continuity - Question 25

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