Exercise 10.1 Class 12 Maths Vector Algebra

NCERT Solutions Class 12 Maths Chapter 10 Ex 10.1 | LearnCBSEHub

💡 Key Concepts

Scalar: A quantity characterized by magnitude only (e.g., mass, temp).
Vector: A quantity characterized by both magnitude and direction (e.g., velocity, force).
Collinear Vectors: Vectors parallel to the same line, regardless of magnitude or direction.
Equal Vectors: Vectors having the same magnitude AND same direction.

Question 01

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

Solution Steps:

Draw a Cartesian plane with North (N), South (S), East (E), and West (W).
“30° east of north” means we start at North and rotate 30° towards East.
Draw a vector $\vec{OP}$ starting from origin $O$ with length representing 40 km (Scale: 1 unit = 10 km).

Note: The angle is made with the vertical Y-axis (North).

Question 02

Classify the following measures as scalars and vectors.

Quantity	Type	Reasoning
(i) 10 kg	Scalar	Mass involves only magnitude.
(ii) 2 meters north-west	Vector	Has magnitude (2m) and direction (NW).
(iii) 40°	Scalar	Angle is a magnitude.
(iv) 40 watt	Scalar	Power has only magnitude.
(v) $10^{-19}$ coulomb	Scalar	Electric charge has only magnitude.
(vi) 20 m/s²	Vector	Acceleration involves direction.

Question 03

Classify the following as scalar and vector quantities.

Quantity	Type	Reasoning
(i) Time period	Scalar	Time has magnitude only.
(ii) Distance	Scalar	Path length (no specific direction).
(iii) Force	Vector	Push/Pull needs direction.
(iv) Velocity	Vector	Speed with direction.
(v) Work done	Scalar	Dot product of Force and Displacement.

Question 04

In Fig 10.6 (a square), identify the following vectors.

Assumption based on standard NCERT Figure: Square with vectors $\vec{a}, \vec{b}, \vec{c}, \vec{d}$ forming sides. Usually $\vec{a}$ (top) and $\vec{d}$ (left) originate from top-left.

(i) Coinitial Vectors: Vectors having the same initial point.

Answer: $\vec{a}$ and $\vec{d}$

(ii) Equal Vectors: Vectors having same magnitude and same direction.

Answer: $\vec{d}$ and $\vec{b}$ (Assuming both point downwards).

(iii) Collinear but not equal: Parallel vectors with different magnitude or opposite direction.

Answer: $\vec{a}$ and $\vec{c}$ (Parallel supports but opposite directions).

Question 05

Answer the following as true or false.

(i) $\vec{a}$ and $-\vec{a}$ are collinear.
TRUE
They lie on the same line or parallel lines, just opposite in direction.
(ii) Two collinear vectors are always equal in magnitude.
FALSE
Collinearity refers to parallel support, not length. Example: $\vec{a}$ and $2\vec{a}$.
(iii) Two vectors having same magnitude are collinear.
FALSE
They can have same length but different directions (e.g., sides of a triangle).
(iv) Two collinear vectors having the same magnitude are equal.
FALSE
They could be in opposite directions ($\vec{a}$ and $-\vec{a}$ are collinear and equal in magnitude, but not equal vectors).