List of Solved Numerical Problems of Unit-2: Vectors and Equilibrium HSSC-I (class 11) Physics (Punjab Curriculum Textbook Board, Lahore) With Verified Answers

Numerical Problems 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)

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Numerical Problems 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)

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

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Numerical Problems 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°]

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Numerical Problems 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)

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Numerical Problems 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}` and (b) `\vec {D}` =3`\vec {A}`- 2`\vec {B}`

(Ans: 5.1, 349° ; 17, 90°)

(Ans: 4.1) 

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Numerical Problems 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°)

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Numerical Problems 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)

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Numerical Problems 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.

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Numerical Problems 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 )

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Numerical Problems 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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Numerical Problems 2.12: The torque or turning effect of force about a given point is given by r x F where r is the vector from the given point to the point of application of F. Consider a force F = - 3 `\hat {i}` + `\hat {j}` +5`\hat {k}` (newton) acting on the point 7`\hat {i}` + 3 `\hat {j}` + `\hat {k}` (m). What is the torque in N m about the origin?

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Numerical Problems 2.13: The line of action of force. `\vec {F}` = `\hat {i}` - 2`\hat {j}` , passes through a point whose position vector is (-`\hat {j}` + `\hat {k}`). Find 

(a) the moment of `\vec {F}` about the origin, 

(b) the moment of `\vec {F}` about the point of which the position vector is `\hat {i}` + `\hat {k}`.

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Numerical Problems 2.14: The magnitude of dot and cross products of two vectors are 6√3 and 6 respectively. Find the angle between the vectors (Ans: 30°) 

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Numerical Problems 2.15: A load of 10.0 N is suspended from a clothes line. This distorts the line so that it makes an angle of 15° with the horizontal at each end. Find the tension in the clothes line. [Ans: 19.3N]

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