Learn Maths Vectors, Class 12 Maths Vectors Exercise, Free Online Vectors Lessons

Class 12 Maths Study Material

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Vectors

If the position vectors of the points A, B, C be vector a, vector b, [3(vector a) - 2(vector b)] respectively, then the points A, B, C are?

a) Non-collinear
b) Collinear
c) Forming a right angled triangle
d) None of these

✔Answer

Correct Answer Is : Collinear

Solution Is :

Let vector a, vector b, and vector c be three non-zero vectors, no two of which are collinear. If the [vector a + 2(vector b)] is collinear with vector c and [vector b + 3(vector c)] is collinear with vector a, then [vector a + 2(vector b) + 6(vector c)] is equal to ?

a) λ (vector a)
b) Zero vector
c) λ (vector b)
d) λ (vector c)

✔Answer

Correct Answer Is : Zero vector

Solution Is :

Vector a and vector b are two non-collinear vectors, then [x(vector a) + y(vector b)] (where x and y are scalars) represents a vector which is?

a) Parallel to vector a
b) Parallel to vector b
c) Coplanar with vector a and vector b
d) None of these

✔Answer

Correct Answer Is : Coplanar with vector a and vector b

Solution Is :

A, B, C, D, E are five coplanar points, then vector DA + vector DB + vector DC + vector AE + vector BE + vector CE = is equal to?

a) 4(vector DE)
b) 2(vector DE)
c) Vector DE
d) 3(vector DE)

✔Answer

Correct Answer Is : 3(vector DE)

Solution Is :

Area of the parallelogram whose diagonals are vector a and vector b is?

a) (vector a) . (vector b)
b) 1/2 |vector a * vector b|
c) |vector a * vector b|
d) Vector a + vector b

✔Answer

Correct Answer Is : 1/2 |vector a * vector b|

Solution Is :

If vector a and vector b are unit vectors such that (vector a * vector b) is also a unit vector, then the angles between vector a and vector b is?

a) π
b) π/2
c) π/3
d) 0

✔Answer

Correct Answer Is : π/2

Solution Is :

The number of vectors of unit length perpendicular to vectors vector a = (1, 1, 0) and vector b = (0, 1, 1) is?

a) Two
b) One
c) Three
d) Infinite

✔Answer

Correct Answer Is : Two

Solution Is :

If (vector a * vector b)^2 + [(vector a) . (Vector b)]^2 = 144 and |vector a| = 4, then |vector b| = ?

a) 3
b) 12
c) 8
d) 16

✔Answer

Correct Answer Is : 3

Solution Is :

[2(vector a) + 3(vector b)] * [5(vector a) + 7(vector b)] = ?

a) 7(vector a) + 10(vector b)
b) Vector a + vector b
c) Vector b * vector a
d) Vector a * vector b

✔Answer

Correct Answer Is : Vector b * vector a

Solution Is :

Let vector a, vector b, vector c be three vectors such that vector a ≠0, and [(vector a * vector b) = 2(vector a) * vector c], |vector a| = |vector c| = 1, |vector b| = 4 and |vector b * vector c| = √15. If [vector b - 2(vector c)] = λ (vector a), then λ is equal to?

a) -2
b) ±4
c) 1
d) 3

✔Answer

Correct Answer Is : ±4

Solution Is :

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Class 12 Maths Study Material

Vectors

If the position vectors of the points A, B, C be vector a, vector b, [3(vector a) - 2(vector b)] respectively, then the points A, B, C are?

Correct Answer Is : Collinear

Solution Is :

Let vector a, vector b, and vector c be three non-zero vectors, no two of which are collinear. If the [vector a + 2(vector b)] is collinear with vector c and [vector b + 3(vector c)] is collinear with vector a, then [vector a + 2(vector b) + 6(vector c)] is equal to ?

Correct Answer Is : Zero vector

Solution Is :

Vector a and vector b are two non-collinear vectors, then [x(vector a) + y(vector b)] (where x and y are scalars) represents a vector which is?

Correct Answer Is : Coplanar with vector a and vector b

Solution Is :

A, B, C, D, E are five coplanar points, then vector DA + vector DB + vector DC + vector AE + vector BE + vector CE = is equal to?

Correct Answer Is : 3(vector DE)

Solution Is :

Area of the parallelogram whose diagonals are vector a and vector b is?

Correct Answer Is : 1/2 |vector a * vector b|

Solution Is :

If vector a and vector b are unit vectors such that (vector a * vector b) is also a unit vector, then the angles between vector a and vector b is?

Correct Answer Is : π/2

Solution Is :

The number of vectors of unit length perpendicular to vectors vector a = (1, 1, 0) and vector b = (0, 1, 1) is?

Correct Answer Is : Two

Solution Is :

If (vector a * vector b)^2 + [(vector a) . (Vector b)]^2 = 144 and |vector a| = 4, then |vector b| = ?

Correct Answer Is : 3

Solution Is :

[2(vector a) + 3(vector b)] * [5(vector a) + 7(vector b)] = ?

Correct Answer Is : Vector b * vector a

Solution Is :

Let vector a, vector b, vector c be three vectors such that vector a ≠0, and [(vector a * vector b) = 2(vector a) * vector c], |vector a| = |vector c| = 1, |vector b| = 4 and |vector b * vector c| = √15. If [vector b - 2(vector c)] = λ (vector a), then λ is equal to?

Correct Answer Is : ±4

Solution Is :

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