# Position Vector

## Trending Questions

**Q.**A bird moves from point A (1, −2, 3) to B (4, 2, 3). If the speed of the bird is 10 m/s, then the velocity vector of the bird is:

- 5(^i−2^j+3^k) m/s
- (6^i+8^j) m/s
- 5(4^i+2^j+3^k) m/s
- (0.6^i+0.8^j) m/s

**Q.**Ship A is sailing towards north-east with velocity →v=30^i+50^j km/h, where ^i points east and ^j points north. Ship B at a distance of 80 km east and 150 km north of ship A is sailing towards the west at 10 km/h. A will be at minimum distance from B in

- 4.2 h
- 2.2 h
- 2.6 h
- 3.2 h

**Q.**The coordinates of the positions of particles of mass 7, 4 and 10 gm (1, 5, -3), (2, 5, 7) and (3, 3, -1) cm respectively. The position of the centre of mass of the system would be

**Q.**

A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn.

The coordinates(meters) of the rabbit's position as function of time t(seconds) are given by

x(t)=−t22+5t+20 And y(t)=t2−10t+30

(a)At t=10s, what is the rabbot's position vector →r in unit-vector notation and in magnitude-angle notation?

**Q.**At time t=0 s, a particle starts from rest at position (4 m, 8 m). It starts moving towards the positive x-axis with a constant acceleration of 2 m/s2. After 2 s, it undergoes an additional acceleration of 4 m/s2 in the positive y-direction. Find the coordinates of the particle (in m) after the next 5 s.

- (58, 6)
- (−53, 58)
- (53, 58)
- (58, −6)

**Q.**The position vector of point B (8, 4) with respect to point A (3, 7) is

- 8i + 4j
- 3i + 7j
- 11i + 11j
- 5i – 3j

**Q.**A bird moves from point A (1, −2, 3) to B (4, 2, 3). If the speed of the bird is 10 m/s, then the velocity vector of the bird is:

- 5(^i−2^j+3^k) m/s
- 5(4^i+2^j+3^k) m/s
- (0.6^i+0.8^j) m/s
- (6^i+8^j) m/s

**Q.**Point (4, 0) lies on ________.

- →YO
- →XO
- →OX
- →OY

**Q.**Two cars A and B move on a straight road with constant velocity. When they move in same direction, they come close by 8 m in 10 s and when they move in opposite direction towards each other, they come close by 20 m in 1 s. The speed of the cars A and B (in m/s) respectively are

- 9.6 and 10.4
- 10.4 and 9.6
- 20.8 and 10.4
- 10.4 and 20.8

**Q.**Two cars A and B move on a straight road with constant velocity. When they move in same direction, they come close by 8 m in 10 s and when they move in opposite direction towards each other, they come close by 20 m in 1 s. The speed of the cars A and B (in m/s) respectively are

- 9.6 and 10.4
- 10.4 and 9.6
- 20.8 and 10.4
- 10.4 and 20.8

**Q.**A particle follows uniform motion along line from P (2, 4, 6) to Q(4, 8, 2) with a speed of 12 m/s. Find velocity vector of the particle.

- 2^i+4^j−4^k
- none
- 12(2^i+4^j−4^k)
- 4^i+8^j−8^k

**Q.**Two trains A and B have lengths 800 m and 1000 m respectively and are moving with the velocity of 25 m/s and 15 m/s respectively. At time t=0, engine of train A is just behind tail of train B. Find the time when train A completely overtake train B ?

- 10 sec
- 100 sec
- 18 sec
- 180 sec

**Q.**Ship A is sailing towards north-east with velocity →v=30^i+50^j km/h, where ^i points east and ^j points north. Ship B at a distance of 80 km east and 150 km north of ship A is sailing towards the west at 10 km/h. A will be at minimum distance from B in

- 4.2 h
- 2.6 h
- 3.2 h
- 2.2 h

**Q.**

Find the resultant of the given vectors.

Cannot add as is not on origin

**Q.**A wheel of radius r rolls without slipping on the ground, with speed v. When it is at a point P, a piece of mud flies off tangentially from its highest point, lands on the ground at point Q. The distance PQ is:

- 2v√(r/g)
- 2√2v√(r/g)
- 4v√(r/g)
- v√(r/g)

**Q.**A particle moves along the x-axis with acceleration a = 6(t- 1), where t is in seconds. If the particle is initially at the origin and moves along the positive x-axis with v0 = 2 m/s, analyze the motion of the particle.

**Q.**If ¯¯¯p=^i−2^j+^k and ¯¯¯q=^i+4^j−2^k are position vectors of points P and Q, find the position vector of the point R which divides segment PQ internally in the ratio 2:1

**Q.**A particle starts from rest at the origin and moves along X-axis with acceleration a=12−2t. The time after which the particle arrives at the origin is (in seconds)

- 12
- 17
- 18
- 14

**Q.**The position vectors of the points A, B, C and D are 3^i−2^j−^k, 2^i+3^j−4^k, −^i+^j+2^k and 4^i+5^j+λ^k respectively. If the points A, B, C and D lie on a plane, find the value of λ.

**Q.**Two identical particles are located at →x and →y with reference to the origin of three dimensional co-ordinate system. The position vector of centre of mass of the system is given by

- →x−→y
- →x+→y2
- →x−→y2
- (→x−→y)

**Q.**If C is the midpoint of AB and P is any point outside AB, then −−→PA+−−→PB=

**Q.**If the position vectors of A, B, C, D are 3^i+2^j+^k, 4^i+5^j+5^k, 4^i+2^j−2^k, 6^i+5^j−^k respectively then the position vector of the point of intersection of ¯AB and ¯CD is

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

**Q.**At time t=0 s, a particle starts from rest at position (4 m, 8 m). It starts moving towards the positive x-axis with a constant acceleration of 2 m/s2. After 2 s, it undergoes an additional acceleration of 4 m/s2 in the positive y-direction. Find the coordinates of the particle (in m) after the next 5 s.

- (58, 6)
- (53, 58)
- (−53, 58)
- (58, −6)

**Q.**

A watermelon seed has the following coordinates: x=-5.0 m, y=9.0 m and z=0 m. Find its position vector

(a) In unit-vector notation and as

(b) A magnitude and

(c) An angle relative to the positive direction of the x-axis

**Q.**The P.V.′s of the vertices of a △ABC are ¯i+¯j+¯k, 4¯i+¯j+¯k, 4¯i+5¯j+¯k. The P.V. of the circumcentre of △ABC is

- 52¯i+3¯j+¯k
- 5¯i+32¯j+¯k
- ¯i+¯j+¯k
- 5¯i+3¯j+12¯k

**Q.**The position vectors of P and Q are respectively a and b. If R is a point on PQ, PQ such that PR=5PQ, then the position vector of R is

- 5b+4a
- 4b−5a
- 5b−4a
- 4b+5a

**Q.**If ^i, ^j, ^k are positive vectors of A, B, C and →AB=→CX, then positive vector of X is

- −^i+^j+^K
- ^i−^j+^K
- ^i+^j−^K
- ^i+^j+^K

**Q.**Find the position vectors of a point R which divides the line joining two points P and Q whose position vectors are 2→a+3→b and →a−3→b respectively, externally in the ratio 1:2. Also, show that P is the midpoint of the line segment R.

**Q.**If →b and →c are the position vectors of the points B and C respectively, then the position vector of the point D such that −−→BD=4−−→BC is

- 4(→c−→b)
- 4→c−3→b
- −4(→c−→b)
- 4→c+3→b

**Q.**L and M are two points with position vectors 2→a−→b and →a+2→b respectively. Write the position vector of a point N which divides the line segment LM in the ratio 2 : 1 externally.