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INDIAN NAVY SAILORS Numerical Ability Study Material

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Vectors

If ABCD is parallelogram with AC and BD as diagonals, then (vector AC - vector BD) = ?

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

✔Answer

Correct Answer Is : 2(vector AB)

Solution Is :

If vector c = 2(vector a) - 3(vector b) and 2(vector c) = 3(vector a) + 4(vector b), then vector c and vector a are?

a) At right angles
b) Like parallel vectors
c) Unlike parallel vectors
d) None of these

✔Answer

Correct Answer Is : Like parallel vectors

Solution Is :

Vectors (p, q) and (5, 1) are parallel, if

a) Pq = 5
b) Q = 5 p
c) P + q = 5
d) P = 5 q

✔Answer

Correct Answer Is : P = 5 q

Solution Is :

In a triangle ABC, if 2(vector AC) = 3(vector CB), then 2(vector OA) + 3(vector OB) equals?

a) 5(vector OC)
b) Vector OC
c) [-(vector OC)]
d) None of these

✔Answer

Correct Answer Is : 5(vector OC)

Solution Is :

ABCDEF is a regular hexagon and vector AB = vector a, vector BC = vector b and vector CD = vector c, then vector AE is?

a) Vector c + vector a
b) Vector a + vector b + vector c
c) Vector b + vector c
d) Vector a + vector b

✔Answer

Correct Answer Is : Vector b + vector c

Solution Is :

If three points A, B and C have position vectors (1, x, 3), (3, 4, 7) and (y, -2, -5) respectively and if they are collinear, then (x, y) = ?

a) (-2, 3)
b) (2, -3)
c) (2, 3)
d) (-2, -3)

✔Answer

Correct Answer Is : (2, -3)

Solution Is :

In a triangle ABC, vector AB = vector a, vector AC = vector c, vector BC = vector b, then ?

a) Vector a + vector b + vector c = 0
b) Vector a + vector b - vector c = 0
c) Vector a - vector b + vector c = 0
d) (-vector a + vector b + vector c) = 0

✔Answer

Correct Answer Is : Vector a + vector b - vector c = 0

Solution Is :

If vector a and vector b are two non-zero and non-collinear vectors, then vector a + vector b and vector a - vector b are?

a) Linearly dependent vectors
b) Linearly dependent and independent vectors
c) Linearly independent vectors
d) None of these

✔Answer

Correct Answer Is : Linearly independent vectors

Solution Is :

If a = (1, -1) and b = (-2, m) are two collinear vectors, then m =?

a) 3
b) 4
c) 0
d) 2

✔Answer

Correct Answer Is : 2

Solution Is :

If C is the midpoint of AB and P is any point outside AB, then ?

a) Vector PA + vector PB = 2(vector PC)
b) Vector PA + vector PB = vector PC
c) Vector PA + vector PB + vector PC = zero vector
d) Vector PA + vector PB + 2(vector PC) = zero vector

✔Answer

INDIAN NAVY SAILORS Numerical Ability Study Material

Vectors

If ABCD is parallelogram with AC and BD as diagonals, then (vector AC - vector BD) = ?

Correct Answer Is : 2(vector AB)

Solution Is :

If vector c = 2(vector a) - 3(vector b) and 2(vector c) = 3(vector a) + 4(vector b), then vector c and vector a are?

Correct Answer Is : Like parallel vectors

Solution Is :

Vectors (p, q) and (5, 1) are parallel, if

Correct Answer Is : P = 5 q

Solution Is :

In a triangle ABC, if 2(vector AC) = 3(vector CB), then 2(vector OA) + 3(vector OB) equals?

Correct Answer Is : 5(vector OC)

Solution Is :

ABCDEF is a regular hexagon and vector AB = vector a, vector BC = vector b and vector CD = vector c, then vector AE is?

Correct Answer Is : Vector b + vector c

Solution Is :

If three points A, B and C have position vectors (1, x, 3), (3, 4, 7) and (y, -2, -5) respectively and if they are collinear, then (x, y) = ?

Correct Answer Is : (2, -3)

Solution Is :

In a triangle ABC, vector AB = vector a, vector AC = vector c, vector BC = vector b, then ?

Correct Answer Is : Vector a + vector b - vector c = 0

Solution Is :

If vector a and vector b are two non-zero and non-collinear vectors, then vector a + vector b and vector a - vector b are?

Correct Answer Is : Linearly independent vectors

Solution Is :

If a = (1, -1) and b = (-2, m) are two collinear vectors, then m =?

Correct Answer Is : 2

Solution Is :

If C is the midpoint of AB and P is any point outside AB, then ?

Correct Answer Is : Vector PA + vector PB = 2(vector PC)

Solution Is :

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