JEE Questions for Maths Vector Algebra Quiz 1

Out of the following which one is not true

0%
0%
2)
0%
0%

0%
3 sq units
0%
4 sq units
0%
16 sq units
0%
9 sq units

Given that, |a|= 3, |b|= 4, |a ×b| = 10, then |a . b|² is equal to

0%
88
0%
44
0%
22
0%
None of these

0%
a
0%
2a
0%
3a
0%
0

0%
0%
2)
0%
0%

0%
8 units
0%
9 units
0%
10 units
0%
11 units

0%
{a, b2, c3}
0%
{a, b2, c4}
0%
{a, b1, c1}
0%
{a, b1, c2}

0%
√18
0%
√72
0%
√33
0%
√45

If the position vectors of the vertices of ∆ABC are
Maths-Vector Algebra-58585.png

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right angle and isosceles
0%
right angled but not isosceles
0%
isosceles but not right angled
0%
equilateral

If the vectors a + λb + 3c, – 2a + 3b – 4c and a – 3b + 5c are coplanar, then the value of λ is

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2
0%
–1
0%
1
0%
–2

If the position vector of A with respect to O is
Maths-Vector Algebra-58588.png

0%
0%
2)
0%
0%

If a, b, c are three non - coplanar vectors and p, q, r reciprocal vectors, then (la + mb + nc). (lp + mq + nr) is equal to

0%
l + m + n
0%
l3 + m3 + n3
0%
l2 + m2 + n2
0%
None of these

Let u, v and w be vectors such that u + v + w = 0. If |u| = 3 |v| = 4 and |w| = 5, then u.v + v.w + w.u is equal to

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0
0%
–25
0%
25
0%
50
0%
47

0%
sin-1 (1/9)
0%
cos-1 (8/9)
0%
sin-1 (8/9)
0%
cos-1 (1/9)

If a, b and c are perpendicular to b + c, c + a and a + b, respectively and if |a + b| = 6, |b + c| = 8 and |c + a| = 10, then |a + b + c| is equal to

0%
5√2
0%
50
0%
10√2
0%
10

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

0%
3
0%
9
0%
20
0%
None of these

If x + y + z = 0, |x| = |y| = |z|= 2 and θ is angle between y and z, then the value of cosec² θ is

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4/3
0%
5/3
0%
1/3
0%
1

0%
15/4
0%
15/2
0%
15
0%
15√3/2
0%
15√3

0%
4√6 units
0%
1/2 (√sq units
0%
√6/2 sq units
0%
√6 units

The magnitude of cross product of two vectors is √3 times the dot product. The angle between the vector is

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π/6
0%
π/3
0%
π/2
0%
π/4

0%
√57
0%
√39
0%
12
0%
17

Area of diagonals is, ..., where diagonals are
Maths-Vector Algebra-58608.png

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√21.5
0%
√31.5
0%
√28.5
0%
√38.5

0%
a = 3, b = 1
0%
a = 9, b = 1
0%
a = 3, b = 3
0%
a = 9, b = 3

If |a × b| = 4 and |a ∙ b|= 2, then |a|² |b|² is equal to

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6
0%
2
0%
20
0%
8

If r ∙ a = r ∙ b = r ∙ c = 0 for some non -zero vector r, then the value of [a b c] is

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

0%
2
0%
1
0%
3
0%
–1
0%
0

Volume of the parallelopiped having vertices at O ≡ (0, 0, 0), A ≡ (2, –2, 1), B ≡ (5, –4,and c ≡ (1, –2,is

0%
5 cu units
0%
10 cu units
0%
15 cu units
0%
20 cu units

If the volume of the parallelopiped with a, b and c as coteminous edges is 40 cu units, then the volume of the parallelopiped having b + c, c + a and a + b as coterminous edges in cubic units is