JEE Questions for Maths Vector Algebra Quiz 3

The position vector of mid - point lying on the line joining the points whose positions vectors are
Maths-Vector Algebra-58736.png

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2)
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0

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2)
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I . Two non - zero, non - collinear vectors are linearly independent .
II. Any three coplanar vectors are linearly dependent.
Which of the above statements is/ are correct ?

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Only I
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Only II
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Both I and II
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Neither I nor II

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2)
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The length of longer diagonal of the parallelogram constructed on 5a + 2b and a - 3b, if it is given that |a| = 2√2, |b| = 3 and the angle between a and b is π/4 is

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15
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√113
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√593
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√369

If a, b and c are pth, qth and rth terms of a GP, then the vectors log
Maths-Vector Algebra-58753.png

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equal
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parallel
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perpendicular
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None of these

If a and b are two unit vectors inclined at an angle π/3, then the value of |a + b| is

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equal to
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greater than 1
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equal to 0
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less than 1

If a ∙ b = 0 and a + b makes an angle of 60^o with a, then

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|a| = 2|b|
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2|a| = |b|
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|a| = √3 |b|
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|a| = |b|
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√3 |a| = |b|

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π/2
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π/5
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π/6
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π/4
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π/3

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√7
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√3
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7
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3
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7√3

If a ⊥ b, |a|= 1 and if (a + 3b).(2a – b) = –10, then |b| is equal to

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1
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3
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2
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4

If a, b and c are three non - zero vectors such that each one of them being perpendicular to the sum of the other two vectors, then the value of |a + b + c|² is

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|a|2 + |b|2 + |c|2
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|a| + |b| + |c|
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2(|a|2 + |b|2 + |c|2)
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1/2 (|a|2 + |b|2 + |c|2)
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0

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93
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97
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87
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90

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|a + b|< 1
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|a + b | > 1
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|a – b| < 1
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|a – b| > 1

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2)
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0%

If a, b and c are unit vectors satisfying |a – b|² + |b – c|² + |c – a|² = 9, then |2a + 5b + 5c| is equal to

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3
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4
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2
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5

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π/6
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π/2
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π/3
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π/4

Let ABCD be a parallelogram such that AB = q, AD = p and ∠BAD be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by

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2)
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0%

If a + b + c = 0 and |a| = 3, |b| = 5, |c| = 7, then angle between a and b is

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π/3
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π/6
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π/4
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π

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2)
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If P, Q, R and S are the points on the plane with position vectors
Maths-Vector Algebra-58781.png

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parallelogram, which is neither a rhombus nor a rectangle
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square
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rectangle but not a square
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rhombus but no a square

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8/9
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√17/9
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1/9
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4√5/9

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(–3, 2)
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(2, –3)
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(–2, 3)
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(3, –2)

If p, q and r perpendicular to q + r, r + p and p + q, respectively and if |p + q|= 6, |q + r|= 4√3 and |r + p|=4, then |p + q+ r| is

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5√2
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10
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15
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5
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25

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3
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4
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5
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6

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2)
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If a∙b = – |a||b|, then the angle between a and b is

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45o
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180o
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90o
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60o

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2
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3
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4
0%
5

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18
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15
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12
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9

If u₁ and u₂ be vectors of unit length and θ be the angle between them, then 1/2 |u₂ – u₁| is

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sin θ
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sin θ/2
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cos θ
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cos θ/2

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π/4
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π/3
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π/2
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3π/2

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–7 < λ < 1
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λ > 1
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1 < λ < 7
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–5 < λ < 1

If x and y are unit vectors and x. y = 0, then

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|x + y| = 1
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|x + y| = √3
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|x + y | = 2
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|x + y| = √2

A parallelogram is constructed on the vectors a = 3α – β, b = α + 3β. If |α| = |β| = 2 and the angle between α and β is π/3, then the length of a diagonal of the parallelogram is

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4√5
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4√3
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4√17
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None of these

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c < 0
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0 < c < 4/3
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– 4/3 < c < 0
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c > 0

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10 units
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–10 units
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9 units
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–9 units
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None of these

A vector which is a linear combination of the vectors
Maths-Vector Algebra-58802.png

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Unit vector which is perpendicular to both the vectors
Maths-Vector Algebra-58808.png

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2)
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A unit vector in XY - plane makes an angle of 45^o with the vector
Maths-Vector Algebra-58825.png

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2)
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None of these

Magnitudes of vectors a, b and c are 3, 4, 5 respectively. If a and b + c, b and c + a, c and a + b are mutually perpendicular, then magnitude of a + b + c is