12th NCERT Vector Algebra Exercise 10.1 Questions 5

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Question (1)

Represent graphically a displacement of 40km, 30° east of north

Solution

Displacement 40 km, 30 ° East of North Displacement vector $\overrightarrow {OA} $ (say) such that $\left| {\overrightarrow {OA} } \right|$ = 40 (given) and vector $\overrightarrow {OA} $ makes an angle 30 ° with North in East-North quadrant.

Question (2)

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 m/s²

Solution

i) 10 kg is a measure of mass, it has no direction, it is magnitude only and therefore it is a scalar.
(ii) 2 meters North-West us a measure of velocity. It has magnitude and direction both and hence it is a vector.
(iii) 40° is a measure of angle. It has no direction, it has magnitude only. Therefore it is a scalar.
(iv) 40 Watt is a measure of power. It has no direction, only magnitude and therefore, it is a scalar.
(v) coulomb is a measure of electric charge and it has magnitude only, therefore, it is a scalar.
(vi) 20 m/sec² is a measure of acceleration. It is a measure of rate of change of velocity, therefore, it is a vector.

Question (3)

Classify the following as scalar and vector quantities.
(i) time period     (ii) distance
(iii) force    (iv) velocity
(v) Work done

Solution

(i) Time-scalar
(ii) Distance-scalar
(iii) Force-vector
(iv) Velocity-vector
(v) Work done-scalar

Question (4)

In figure 10.6 (a squar), identify the following vectors

(i) Coinitial     (ii) Equal
(iii) Collinear but not equal

Solution

(i) $\overrightarrow a $ and have same initial point and therefore coinitial vectors.
(ii) $\overrightarrow b $ and $\overrightarrow d $ have same direction and same magnitude. Therefore $\overrightarrow b $ and $\overrightarrow d $ are equal vectors.
(iii) $\overrightarrow a $ and have parallel support, so that they are collinear. Since they have opposite directions, they are not equal. Hence and are collinear but not equal.

Question (5)

Answer the following as true or false
(i) $\overrightarrow a $ and $\overrightarrow a $ are collinear
(ii) Two collinear vectors are always equal in magnitude
(iii) Two vectors haviing same same magnitude are collinear.
(iv) Two collinear vectors having the same magnitude magnitude are equal

Solution

(i) True.
(ii) False. [∵ $\overrightarrow a $ and 2$\overrightarrow a $ are collinear vectors but $\left| {2\overrightarrow a } \right| = 2\overrightarrow a $ ]
(iii) False. [∵ \[\left| {\widehat i} \right| = \left| {\widehat j} \right| = 1\] but $\widehat i$ and $\widehat j$ are vectors along x-axis (OX) and y-axis (OY) respectively]
(iv) False. [ Vectors $\overrightarrow a $ and $ - \overrightarrow a \left\{ { = \left( { - 1} \right)\overrightarrow a = m\overrightarrow a } \right\}$ are collinear vectors and but we know that $\overrightarrow a \ne - \overrightarrow a $ because their directions are opposite.]