# Vectors

## Trending Questions

**Q.**Two vectors A and B have equal magnitude. If the magnitude of (A+B) is ′n′ times the magnitude of (A−B), then angle between vectors A and B is

- sin−1(n2−1n2+1)
- sin−1(n−1n+1)
- cos−1(n2−1n2+1)
- cos−1(n−1n+1)

**Q.**Three particles P, Q and R are moving along the vectors →A=^i+^j, →B=^j+^k and →C=−^i+^j respectively. They strike on a point and start to move in different directions. Now particle P is moving normal to the plane which contains vector →A and →B . Similarly, particle Q is moving normal to the plane which contains vector →A and →C . The angle between the direction of motion of P and Q is cos−1(1√x). Then the value of x is

**Q.**

A particle of mass 2 kg moves on a circular path with constant speed 10mm/s find change in speed and magnitude of change in velocity when particle completes half revolution

**Q.**Let the angle between two non-zero vectors →A and →B be 1200 and resultant be →C, then

- ∣∣∣→C∣∣∣ must be equal to ∣∣∣→A−→B∣∣∣

- ∣∣∣→C∣∣∣ must be less than ∣∣∣→A−→B∣∣∣
- ∣∣∣→C∣∣∣ must be greater than ∣∣∣→A−→B∣∣∣
- ∣∣∣→C∣∣∣ may be equal to ∣∣∣→A−→B∣∣∣

**Q.**Two vectors →X and →Y have equal magnitude. The magnitude of (→X−→Y) is n times the magnitude of (→X+→Y). The angle between →X and →Y is:

- cos−1(n2+1n2−1)
- cos−1(n2+1−n2−1)
- cos−1(n2−1−n2−1)
- cos−1(−n2−1n2−1)

**Q.**

An aeroplane is moving in a circular path with a speed 250 km/h what is change in velocity in half revolution

**Q.**

A body is moving with a uniform velocity of 10 m/s on a circular path of diameter 2.0m. calculate

1) the difference between the magnitude of the displacement of the body and the distance covered in half a round and

2) the magnitude of the changes in velocity of the body in half a round.

**Q.**The magnitudes of four pairs of displacement vectors are given. Which pair of displacement vectors cannot be added to give a resultant vector of magnitude 4 cm?

- 1 cm, 1 cm
- 1 cm, 3 cm
- 1 cm, 5 cm
- 1 cm, 7 cm

**Q.**Let →a=^i+^j+^k, →b=^i−^j+^k and →c=^i−^j−^k be three vectors. A vector →v in the plane of →a and →b, whose projection on →c is 1√3, is given by

- ^i−3^j+3^k
- −3^i−3^j−^k
- 3^i−^j+3^k
- ^i+3^j−3^k

**Q.**A point traversed half a circle of radius R=160cm during time interval t=10sec. Calculate the following quantities averaged over that time (a) the mean velocity

**Q.**If the sum of two unit vectors is a unit vector, then magnitude of difference is

- √2
- √3
- 1/√2
- √5

**Q.**The magniude of vectors \(\overrightarrow {OA}, \overrightarrow {OB}\) and \(\overrightarrow {OC}\) In the given figure are equal.\(\overrightarrow {OA}+\overrightarrow {OB}-\overrightarrow {OC}\) with x-axis will be

**Q.**The sum of the magnitudes of two forces is 18 N and the magnitude of their resultant is 12 N. If the resultant makes an angle of 90∘ with the smaller force, then find the magnitude of the forces.

- 5 N, 13 N
- 6 N, 12 N
- None of these
- 10 N, 8 N

**Q.**The sum of the magnitudes of two forces is 18 N and the magnitude of their resultant is 12 N. If the resultant makes an angle of 90∘ with the smaller force, then find the magnitude of the forces.

- 5 N, 13 N
- 6 N, 12 N
- 10 N, 8 N
- None of these

**Q.**Magnitude of resultant of 3 vectors −−→OA, −−→OB, and −−→OC as shown below is

- r
- 2r
- r(1+√2)
- r(√2−1)

**Q.**Part of commentary by a commentator of a race is given. What can you infer about it? "The racing car takes a circular turn at a constant velocity of 84 km per hour. "

- Commentary is right, car can turn at constant velocity.
- Commentary is wrong, velocity does not remain constant while turning.
- Such high speed is not possible.
- None of the above.

**Q.**Magnitude of resultant of 3 vectors −−→OA, −−→OB, and −−→OC as shown below is

- r
- 2r
- r(1+√2)
- r(√2−1)

**Q.**A radioactive element X converts into another stable element Y. Half-life of X is 2h. Initially, only X is present. After time t, the ratio of atoms of X and Y is found to be 1:4. Then t in hours is

- 2
- 4
- between 4 and 6
- 6

**Q.**A radioactive element X converts into another stable element Y. Half life of X is 2 hrs. Initially only X is present. After time t, the ratio of atoms of X and Y is found to be 1:4, then t in hours:

- 4
- 2
- 6
- Between 4 and 6

**Q.**If the sum of two unit vectors is a unit vector, then magnitude of their difference is

- √2
- √3
- 1√2
- √5

**Q.**Two forces each of 10N act at an angle 600 with each other. The magnitude and direction of the resultant with respect to one of the vectors is:

- √10N, 300
- 10√3N, 300
- 10√2N, 1200
- 20N, 1200

**Q.**The resultant of two vectors A and B subtends an angle of 45∘ with either of them. The magnitude of the resultant is

- zero
- √2A
- A
- 2A

**Q.**Let →a=^i+^j+^k, →b=^i−^j+^k and →c=^i−^j−^k be three vectors. A vector →v in the plane of →a and →b, whose projection on →c is 1√3, is given by

- ^i−3^j+3^k
- −3^i−3^j−^k
- 3^i−^j+3^k
- ^i+3^j−3^k

**Q.**The sum of the magnitude of two forces at a point is 16 N. If their resultant is normal to the smaller force and has a magnitude of 8 N. Then two forces are

- 6 N, 10 N
- 8 N, 8 N
- 4 N, 12 N
- 2 N, 14 N

**Q.**If SA and SB represents the displacement of block and plank w.r.t. ground respectively when block seperates, then

- SA=4V√l3g−23l
- SA=4V√lg−23l
- SB=4V√l3g−53l
- SB=4V√lg−13l

**Q.**Part of commentary by a commentator of a race is given. What can you infer about it? "The racing car takes a circular turn at a constant velocity of 84 km per hour. "

- Commentary is right, car can turn at constant velocity.
- Commentary is wrong, velocity does not remain constant while turning.
- Such high speed is not possible.
- None of the above.