Exercise 10.1 Practice
Chapter 10: Vector Algebra – NCERT Solutions
Q1
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Represent graphically a displacement of 40 km, 30° east of north.
Draw a coordinate system with North, South, East, and West directions.
"30° east of north" means measuring 30° from the North axis towards the East.
Draw a vector $\vec{OP}$ starting from the origin $O$ with length representing 40 km (e.g., scale 1 cm = 10 km, so 4 cm length) at an angle of 30° from the North axis towards East.
$\boxed{\text{Vector drawn at 30}^\circ \text{ from North towards East with magnitude 40 km}}$
Q2
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Classify the following measures as scalars and vectors:
(i) 10 kg
(ii) 2 meters north-west
(iii) 40°
(iv) 40 watt
(v) $10^{-19}$ coulomb
(vi) $20 \text{ m/s}^2$
(i) 10 kg
(ii) 2 meters north-west
(iii) 40°
(iv) 40 watt
(v) $10^{-19}$ coulomb
(vi) $20 \text{ m/s}^2$
(i) 10 kg: Mass (Magnitude only) $\rightarrow$ Scalar
(ii) 2 meters north-west: Displacement (Magnitude + Direction) $\rightarrow$ Vector
(iii) 40°: Angle (Magnitude only) $\rightarrow$ Scalar
(iv) 40 watt: Power (Magnitude only) $\rightarrow$ Scalar
(v) $10^{-19}$ coulomb: Charge (Magnitude only) $\rightarrow$ Scalar
(vi) $20 \text{ m/s}^2$: Acceleration (Magnitude + Direction) $\rightarrow$ Vector
$\boxed{\text{(i) Scalar (ii) Vector (iii) Scalar (iv) Scalar (v) Scalar (vi) Vector}}$
Q3
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Classify the following as scalar and vector quantities:
(i) time period
(ii) distance
(iii) force
(iv) velocity
(v) work done
(i) time period
(ii) distance
(iii) force
(iv) velocity
(v) work done
(i) Time period: Scalar
(ii) Distance: Scalar
(iii) Force: Vector
(iv) Velocity: Vector
(v) Work done: Scalar
$\boxed{\text{(i) Scalar (ii) Scalar (iii) Vector (iv) Vector (v) Scalar}}$
Q4
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In Figure (a square), identify the following vectors:
(i) Coinitial
(ii) Equal
(iii) Collinear but not equal
(i) Coinitial
(ii) Equal
(iii) Collinear but not equal
Based on the standard NCERT figure for this question (Square with vectors $\vec{a}, \vec{b}, \vec{c}, \vec{d}$):
(i) Coinitial: Vectors having the same initial point. In the figure, $\vec{a}$ and $\vec{d}$ start from the same vertex.
(ii) Equal: Vectors having same magnitude and direction. $\vec{b}$ and $\vec{d}$ are equal (parallel and same sense).
(iii) Collinear but not equal: Vectors that are parallel but may have different magnitudes or opposite directions. $\vec{a}$ and $\vec{c}$ are parallel but opposite in direction.
$\boxed{\text{(i) } \vec{a} \text{ and } \vec{d} \text{ (ii) } \vec{b} \text{ and } \vec{d} \text{ (iii) } \vec{a} \text{ and } \vec{c}}$
Q5
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Answer the following as true or false:
(i) $\vec{a}$ and $-\vec{a}$ are collinear.
(ii) Two collinear vectors are always equal in magnitude.
(iii) Two vectors having same magnitude are collinear.
(iv) Two collinear vectors having the same magnitude are equal.
(i) $\vec{a}$ and $-\vec{a}$ are collinear.
(ii) Two collinear vectors are always equal in magnitude.
(iii) Two vectors having same magnitude are collinear.
(iv) Two collinear vectors having the same magnitude are equal.
(i) True: They are parallel (opposite directions).
(ii) False: Collinear vectors can have different magnitudes.
(iii) False: They can have different directions (intersecting).
(iv) False: They could be opposite in direction ($\vec{a}$ and $-\vec{a}$).
$\boxed{\text{(i) True (ii) False (iii) False (iv) False}}$