Referring to the AP Inter 2nd Year Maths Study Material Chapter 10 Vector Algebra Exercise 10a Solutions makes it easier to understand complex problems.
AP Inter 2nd Year Maths Vector Algebra Solutions Exercise 10a
I.
Question 1.
Represent graphically a displacement of 40 km, 30° east of north.
Solution:
Given displacement 40 km and 30° East of North direction.
The required vector: Displacement vector \(\overrightarrow{\mathrm{OP}}\) (say) such that \(|\overrightarrow{\mathrm{OP}}|\) = 40 and vector \(\overrightarrow{\mathrm{OP}}\) 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
Solution:
i) 10 kg is a measure of mass and hence a scalar. (∵ 10 kg has no direction, it has only magnitude).
ii) 2 meters North-West is a measure of velocity and hence is a vector.
Question 3.
Classify the following measures as scalars and vectors.
i) 40°
ii) 40 Watt
Solution:
i) 40° is a measure of angle and, therefore, a scalar.i.e. (It has only magnitude)
ii) 40 Watt is a measure of power and hence a scalar, (i.e., 40 watt has no direction)
Question 4.
Classify the following measures as scalars and vectors.
i) 10-19 coulomb
ii) 20m/s2
Solution:
i) 10-19 coulomb is a measure of electric charge and hence a scalar. (It has magnitude only)
ii) 20 m/sec2 is a measure of acceleration and hence a vector.
Question 5.
Classify the following as scalar and vector quantities.
i) time period
ii) velocity
Solution:
i) Time-scalar
ii) Velocity-vector
Question 6.
Classify the following as scalar and vector quantities
i) force
ii) distance
Solution:
i) Force-vector
ii) Distance-scalar
Question 7.
Classify the following as scalar and vector quantities,
i) work done
ii) displacement
Solution:
i) Work done – scalar.
ii) displacement – vector
II.
Question 1.
In the adjacent figure (a square), identify the following vectors.
i) Coinitial
ii) Equal
iii) Collinear but not equal
Solution:
i) \(\vec{a}\) and \(\vec{d}\) have same initial point and hence coinitial vectors.
ii) \(\vec{b}\) and \(\vec{d}\) have same direction and same magnitude.
Hence \(\vec{b}\) and \(\vec{d}\) are equal vectors.
iii) \(\vec{a}\) and \(\vec{c}\) have parallel suports, so that they are collinear. Since they have opposite directions, they are not equal. Hence \(\vec{a}\) and \(\vec{c}\) are collinear but not equal.
Question 2.
Answer the following as true or false.
i) a and -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.
Solution:
i) True. [∵ Collinear vectors has either same or opposite directions)
ii) False. [∵ \(\vec{b}\) and 2\(\vec{b}\) are collinear vectors but \(|2 \overrightarrow{\mathrm{a}}|=2|\overrightarrow{\mathrm{a}}|\)]
iii) False. [∵ \(\hat{\mathbf{i}}=|\hat{\mathbf{j}}|=1\) but vectors \(\hat{\mathbf{i}} \text { and } \hat{\mathbf{j}}\) are not collinear, infact they are perpendicular.
iv) False, [∵ Vectors \(\vec{a}\) and \(\vec{a}\) ≠ \(-\vec{a}\)(= (-1)\(\vec{a}\) = m\(\vec{a}\)) are collinear
vectors and \(|\vec{a}|=\mid-\vec{a}\) but we know that \(\vec{a} \neq-\vec{a}\) because theey are opposite].