2.1:  Suppose, in a rectangular coordinate system, a vector A has its tail at the point P (-2, -3) and its tip at Q (3,9). Determine the distance between these two points. (Ans: 13 Units) 

(Click for verified Solution)


2.2:  A certain corner of a room is selected as the origin of a rectangular coordinate system. If an insect is sitting on an adjacent wall at a point having coordinates (2,1), where the units are in metres, what is the distance of the insect from this corner of the room?

(Ans: 2.2m)



2.3:  What is the unit vector in the direction of the vector A=4 i +3 j ?


2.4: Two particles are located at it `\vec {r₁}` = 3`\hat {i}` + 7`\hat {j}` and `\vec {r₂}` = -2`\hat {i}` + 3`\hat {j}` respectively. Find both the magnitude of the vector `\vec {r₂}` - `\vec {r₁}` and its orientation with respect to the x-axis. [Ans: 6.4, 219°]



2.5: If a vector `\vec {B}` is added to vector  `\vec {A}`, the result is 6`\hat {i}` + `\hat {j}` . If  `\vec {B}` is subtracted from  `\vec {A}`, the result is -4 `\hat {i}` + 7`\hat {j}` . What is the magnitude of vector `\vec {A}`?⃗⃖

(Ans: 4.1)


2.6: Given that `\vec {A}` = 2`\hat {i}` + 3`\hat {j}` and `\vec {B}` = 3`\hat {i}` - 4`\hat {j}` find the magnitude and angle of (a) `\vec {C}` =`\vec {A}`+ `\vec {B}` nd (b) `\vec {D}` =3`\vec {A}`- 2`\vec {B}`

(Ans: 5.1, 349° ; 17, 90°)



2.7: Find the angle between the two vectors, `\vec {A}` = 5`\hat {i}` + `\hat {j}` and `\vec {B}` = 2`\hat {i}` + 4`\hat {j}` (Ans: 52°)


2.8:  Find the work done when the point of application of the force 3`\hat {i}` + 2`\hat {j}` moves in a straight line from the point (2,-1) to the point (6,4). (Ans: 22 units)



2.9: Show that the three vectors `\hat {i}` + `\hat {j}` +`\hat {k}`  , 2`\hat {i}` - 3`\hat {j}` + `\hat {k}`  and 4`\hat {i}` + `\hat {j}` - 5`\hat {k}` are mutually perpendicular.


2.10: Given that `\vec {A}` = `\hat {i}` - 2`\hat {j}` + 3`\hat {k}`   and `\vec {B}` = 3`\hat {i}` - 4`\hat {k}`, find the projection of A on B.  (Ans: -5/9 )



2.11:  Vectors `\vec {A}`, `\vec {b}` and `\vec {C}` are 4 units north, 3 units west and 8 units east, respectively. Describe carefully (a) `\vec {A}` x `\vec {B}` (b) `\vec {A}` x `\vec {C}` (c) `\vec {B}` x `\vec {C}`

[Ans: (a)12 units vertically up (b) 32 units vertically down (c) Zero]

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2.12: 

a) How many seconds are there in 1 year?
b) How many nanoseconds in 1 year?
c) How many years in 1 second?

[Ans. ( a) 3.1536 x 10⁷s, (b) 3.1536 x 10¹⁶ns (c) 3.1 x 10⁻⁸ yr]



2.13: The length and width of a rectangular plate are measured to be 15.3 cm and 12.80 cm, respectively. Find the area of the plate. (Ans: 196 cm²)


2.14: Add the following masses given in kg upto appropriate precision. 2.189, 0.089, 11.8 and 5.32. (Ans: 19.4 kg)



2.15: Find the value of 'g' and its uncertainty using T = 2Ï€ `sqrt\frac {l}{g}` from the following measurements made during an experiment.
Length of simple pendulum l = 100 cm. Time for 20 vibrations = 40.2 s.
Length was measured by a metre scale of accuracy upto 1 mm and time by stop watch of accuracy upto 0.1 s.
(Ans: 9.76 ± 0.06 ms⁻²)




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