Which of the following is a **scalar quantity**?
Analysis & Theory
**Mass** has magnitude only and no direction, so it is a **scalar**.
Which of the following is a **vector quantity**?
Analysis & Theory
**Acceleration** has both **magnitude and direction**, making it a **vector**.
What is the **graphical representation of a vector**?
A
A line with no direction
B
A curve showing magnitude
C
An arrow showing magnitude and direction
Analysis & Theory
Vectors are represented as **arrows** pointing in the direction with the length proportional to magnitude.
Two vectors are said to be **equal** if they have:
A
Same magnitude and same direction
Analysis & Theory
Vectors are **equal** if both **magnitude and direction** are the same.
What is the result of **adding two vectors in the same direction**?
C
Vector with larger magnitude
D
Vector with sum of magnitudes
Analysis & Theory
If two vectors point in the **same direction**, their magnitudes **add up**.
Which law is used to find the **resultant of two vectors** placed head-to-tail?
Analysis & Theory
The **triangle law of vector addition** involves placing vectors **head-to-tail**.
What is the resultant vector according to the **parallelogram law** when two vectors act at 90°?
Analysis & Theory
When vectors act at **90°**, the resultant is found using **Pythagoras theorem**: √(A² + B²).
The **polygon law of vector addition** is useful when:
A
Only two vectors are involved
B
All vectors act at one point in a closed loop
Analysis & Theory
**Polygon law** is used for **more than two vectors** acting consecutively to form a closed polygon.
Which of the following is a **unit vector** along x-direction?
Analysis & Theory
**i** is the **unit vector** in the **x-direction** (|i| = 1).
What is the **dot product** of two perpendicular vectors A and B?
Analysis & Theory
Since cos(90°) = 0, the **dot product** of **perpendicular vectors** is **zero**.
The **cross product** of two parallel vectors is:
Analysis & Theory
Cross product = AB sinθ; for parallel vectors, θ = 0 ⇒ sinθ = 0 ⇒ product = 0.
Which of the following is a **characteristic of dot product**?
Analysis & Theory
**Dot product** gives a **scalar** quantity, not a vector.
If **A = 3i + 4j**, find the **magnitude of A**.
Analysis & Theory
Magnitude = √(3² + 4²) = √(9 + 16) = √25 = **5**.
If vector A = 2i + j and B = i – j, find **A · B**.
Analysis & Theory
A · B = (2×1) + (1×–1) = 2 – 1 = **1**.