# Vector Component

## Trending Questions

**Q.**

The resultant of two vectors $A$ and $B$ is perpendicular to vector $A$ and its magnitude is equal to half the magnitude of vector $B$. The angle between $A$ and $B$ is

$120\xb0$

$150\xb0$

$135\xb0$

None of these

**Q.**

The angle made by the vector A=^i+^j with x- axis is

90∘

22.5∘

30∘

45∘

**Q.**

Two forces, while acting on a particle in opposite; directions, have the resultant of $10N$. If they act at right angles to each other, the resultant is found to be $50N$. Find the two forces.

**Q.**A person pushes a box kept on a horizontal surface with a force of 100 N. In unit vector notation, the force can be expressed as

- 100(^i+^j)
- 100(^i−^j)
- 50√2(^i−^j)
- 50√2(^i+^j)

**Q.**What is the resultant of three coplanar forces 300 N at 0o, 400 N at 30∘ and 400 N at 150∘ with x− axis?

- 500 N
- 700 N
- 1100 N
- 300 N

**Q.**The vector projection of a vector 3^i+4^k on y - axis is

- 5
- 4
- 3
- Zero

**Q.**The sum of the magnitudes of two forces acting at a point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the magnitudes of forces?

- 5, 12
- 12, 13
- 5, 13
- 5, 5

**Q.**

The resultant of two forces $3P$ and $2P$ is $R$, if the first force is doubled, the resultant is also doubled. The angle between the forces is

$\frac{\mathrm{\pi}}{3}$

$\frac{2\mathrm{\pi}}{3}$

$\frac{\mathrm{\pi}}{6}$

$\frac{5\mathrm{\pi}}{6}$

**Q.**

In the given figure two tiny conducting balls of identical mass m and identical charge q hang from non-conducting threads of equal length L. Assume that θ is so small that tan θ≈sin θ, then for equilibrium x is equal to

- (qL22πϵ0mg)1/3
- (q2L2πϵ0mg)1/3
- (q2L24πϵ0mg)1/3
- (q2L4πϵ0mg)1/3

**Q.**→A and →B are two vectors given by →A=2^i+3^j and →B=^i+^j. The magnitude of the component of →A along →B is

- 5√2
- 3√2
- 7√2
- 1√2

**Q.**

If $A,B,C$are the angles of a triangle then find $\mathrm{cos}A+\mathrm{cos}B+\mathrm{cos}C$.

**Q.**

Two forces, F_{1} and F_{2 }are acting on a body. One force is double that of the other force and the resultant is equal to the greater force. Then the angle between the two forces is

$A={\mathrm{cos}}^{-1}\left(\frac{1}{2}\right)$

$A={\mathrm{cos}}^{-1}\left(\frac{-1}{2}\right)$

$A={\mathrm{cos}}^{-1}\left(\frac{-1}{4}\right)$

$A={\mathrm{cos}}^{-1}\left(\frac{1}{4}\right)$

**Q.**What is the maximum number of rectangular components into which a vector can be split?

- 2
- 3
- 4
- Infinite

**Q.**Vector →A is of length 2 cm and makes an angle 60∘ with the x -axis in the first quadrant. Vector →B is of length 2 cm and 60∘ below the x-axis in the fourth quadrant. The sum →A+→B is a vector of magnitude in cm.

- 2 along +y-axis
- 2 along +x-axis
- 1 along −x-axis
- 2 along −x-axis

**Q.**Two vectors acting in the opposite directions have a resultant of 10 units. If they act at right angles to each other, then the resultant is 50 units. Calculate the magnitude of two vectors.

- 40, 30
- 50, 40
- 40, 50
- 30, 40

**Q.**Component of 3^i+4^j perpendicular to ^i+^j and in the same plane as that of 3^i+4^j is

- 12(−^i+^j)
- 13(^i−^j)
- 14(−^i+^j)
- 15(^i−^j)

**Q.**Two bodies of masses 1 kg and 3 kg have position vectors ^i+2j+k and −3^i−2^j+^k respectively. The centre of mass of this system has a position vector

- −2^i+2^k
- −2^i−^j+^k
- −^i+^j+^k
- −2^i−^j+2^k

**Q.**The angle between the vectors →A and →B is θ. The triple product →A.(→B × →A) is equal to

- A2 B sin2θ
- A2 B sinθ cosθ
- A2 B cos2θ
- \N

**Q.**

The resultant force of $5N$ and $10N$ cannot be

$12N$

$8N$

$4N$

$5N$

**Q.**The resultant of →P and →Q is perpendicular to →P. What is the angle between →P and →Q

- cos−1(PQ)
- cos−1(−PQ)
- sin−1(PQ)
- sin−1(−PQ)

**Q.**

Which of the following sets of concurrent forces may be in equilibrium

**Q.**The angle between the vector 2^i+4^k and the Y- axis is

- 45∘
- 180∘
- 0∘
- 90∘

**Q.**

Position of a particle in a rectangular-co-ordinate system is (3, 2, 5). Then its position vector will be

5^i+3^j+2^k

3^i+5^j+2^k

3^i+2^j+5^k

None of these

**Q.**What is the maximum number of components into which a vector can be split?

- 2
- 3
- 4
- Infinite

**Q.**A vector in xy - plane has a magnitude of 25 m and magnitude of x - component is 20 m. The angle it makes with the positive x - axis is

- 53∘
- 26∘
- 29∘
- 37∘

**Q.**As shown in figure, the tension in the horizontal cord is 30 N. The weight W and tension in the string OA in Newton are

- 30√3, 30
- 30√3, 60
- 60√3, 30
- None of these

**Q.**

What is i and j in a vector?

**Q.**During the swinging of a simple pendulum,

- The work done by tension force is always zero
- The work done by the gravitational force is zero
- The mechanical energy of the bob remains constant in the presence of air resistance
- The mechanical energy of the bob does not remain constant in the absence of air

**Q.**The horizontal component of a force of 10 N inclined at 30o to vertical is

- 3 N
- 5√3 N
- 5 N
- 10√3 N

**Q.**

What is the simplest type of motion?