no value of m for which vectors are coplanar

perpendicular from the origin to the plane of the triangle does not meet it at the centroid

JEE Questions for Maths Vector Algebra Quiz 2

0%
0
0%
1
0%
|r|
0%
2 |r|

a × [ a × ( a × b) ] is equal to

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( a × a ) ∙ ( b × a )
0%
a ∙ ( b × a ) – b ( a × b )
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[ a ∙ ( a × b ) ] a
0%
( a ∙ a ) ( b × a )

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a
0%
2 a
0%
3a
0%
None of these

If a is vector perpendicular to both b and c, then

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a + (b + c) = 0
0%
a × (b + c) = 0
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a × (b × c) = 0
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a ∙(b × c) = 0

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± 1/7
0%
± 7
0%
± √43
0%
± 1/√43
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± 1/√7

If a, b and c are non - coplanar vectors and if d is such that d = 1/x (a + b + c) and d = 1/y (b + c + d), where x and y are non - zero real numbers, then 1/xy (a + b + c + d) equals

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3c
0%
– a
0%
0
0%
2a

Three non - zero collinear vectors a, b and c are such that a + 3b is collinear with 3b + 2c is collinear with a. Then, a + 3b + 2c is equal to

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0
0%
2a
0%
3b
0%
4c

0%
0%
2)
0%
0%

0%
parallelogram
0%
rectangle
0%
trapezium
0%
square

0%
0%
2)
0%
0%
0%

If S is circumcentre, G is the centroid, O is the orthocentre of ∆ABC, then SA + SB + SC is equal to

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SG
0%
OS
0%
SO
0%
OG

If R², find the unit vector orthogonal to unit vector x = (cos α, sin α)

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(cos α/2, sin α/2)
0%
(–cos α, – sin α)
0%
(– sin α, cos α)
0%
(cos α, sin α)

ABCDEF is a regular hexagon with centre at the origin such that AD + EB + FC = λED. Then, λ is equal to

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2
0%
4
0%
6
0%
3

0%
0%
2)
0%
0%

If 2a + 3b – 5c = 0, then the ration in which c divides AB is

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3 : 2 internally
0%
3 : 2 externally
0%
2 : 3 internally
0%
2 : 3 externally

If C is the mid - point of AB and P is any point outside AB, then

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PA + PB = PC
0%
PA + PB + 2PC = 0
0%
PA + PB – 2PC = 0
0%
PA + PB + PC = 0

Let a, b and c be three non - zero vectors such that no two of these are collinear. If the vector a + 2b is collinear with C, then a + 2b + 6c is equals to

0%
λ a (λ ≠ 0, a scalar )
0%
λ b (λ ≠ 0, a scalar )
0%
λ c (λ ≠ 0, a scalar )
0%
0

0%
0
0%
1
0%
–2
0%
2

If a = (2, 1, –1), b = (1, –1, 0), c = (5, –1, 1), then unit vector parallel to a + b – c but in opposite direction is

0%
0%
2)
0%
0%
None of these

In a quadrilateral ABCD, the point P divides DC in the ration 1 : 2 and Q is the mid - point of AC. If AB + 2AD + BC – 2DC = kPQ, then k is equal to

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–6
0%
–4
0%
6
0%
4

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m3 < m1 < m4 < m2
0%
m3 < m1 < m2 < m4
0%
m3 < m4 < m1 < m2
0%
m3 < m4 < m2 < m1

A, B, C, D, E, and F in that order, are the vertices of a regular hexagon with centre origin. If the position vectors of the vertices A and B are respectively,
Maths-Vector Algebra-58670.png

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0%
2)
0%
0%

0%
1
0%
4
0%
3
0%
no value of m for which vectors are coplanar

0%
0%
2)
0%
0%

The non - zero vectors a, b and c are related by a = 8 b and c = – 7b. Then, the angle between a and c is

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π
0%
0
0%
π/4
0%
π/2

The position vectors of P and Q are respectively, a and b. If R is point on PQ such that PR = 5PQ, then the position vector R is

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5b – 4a
0%
5b + 4a
0%
4b – 5a
0%
4b + 5a

The unit vector in ZOX - plane and making angle 45^o and 60^o, respectively with
Maths-Vector Algebra-58685.png

0%
0%
2)
0%
0%
None of these

If a and b are unit vectors |a + b| = 1, then |a – b| is equal to

0%
√2
0%
1
0%
√5
0%
√3

If A, B and C are the vertices of a triangle whose position vectors are a, b and c respectively and G is the centroid of the ∆ABC, then GA + GB + GC is

0%
0
0%
a + b + c
0%
0%

0%
0%
2)
0%
0%

0%
–40
0%
–20
0%
20
0%
40

If the position vectors of A, B and C are respectively
Maths-Vector Algebra-58701.png

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0
0%
6/41
0%
35/41
0%
1

0%
0%
2)
0%
∆ ABC is a scalene triangle
0%
perpendicular from the origin to the plane of the triangle does not meet it at the centroid

If P is any point with in a ∆ ABC, then PA + CP is equal to

0%
AC + CB
0%
BC + BA
0%
CB + AB
0%
CB + BA

The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vectors is

0%
√3
0%
1 – √3
0%
1 + √3
0%
– √3

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√29
0%
4
0%
√62 – 2√35
0%
√66

0%
0%
2)
0%
0%
0%

If ABCD be a parallelogram and M be the point of intersection of the diagonals. If O is any point, then OA + OB + OC + OD is

0%
3OM
0%
4OM
0%
OM
0%
2OM
0%
1/2 OM

If a = (1, –and b = (–2, m) are two collinear vectors, then m is equal to

0%
2
0%
4
0%
3
0%
0

0%
0%
2)
0%
0%
{2, 7}

Let a, b and c be three non - zero vectors such that no two these are collinear. If the vector a + 2b is collinear with c and b + 3c is collinear with a (λ being some non - zero scalar), then a + 2b + 6c is equal to

0%
λa
0%
λb
0%
λc
0%
0

If a, b and c are the position vectors of the vertices of an equilateral triangle, whose orthocentre is at the origin, then

0%
a + b + c = 0
0%
a2 = b2 + c2
0%
a + b = c
0%
None of these

0%
1 : 2
0%
2 : 3
0%
3 : 4
0%
1 : 4

A vector a has components 2p and 1 with respect to a rectangular Cartesian system. This system is rotated clockwise sense. If this respect to new system, a has components p + 1 and 1, then