NEET Physics: scalar and vector products Practice Questions

Correct answer: C — Zero

Two vectors are orthogonal (perpendicular) if the angle between them is 90°, which implies cos(90°) = 0, making their dot product zero.

Correct answer: C — The area of the parallelogram formed by a⃗ and b⃗

The cross product a⃗ × b⃗ results in a new vector. The magnitude of this resulting vector, |a⃗ × b⃗|, is equal to the area of the parallelogram formed by the vectors a⃗ and b⃗. Since area is a scalar quantity, the magnitude is the scalar result.

Correct answer: D — Cross product (×)

The dot product results in a scalar, while the cross product results in a vector.

Correct answer: A — Anti-commutativity

The property a⃗ × b⃗ = -(b⃗ × a⃗) describes the anti-commutative nature of the cross product.

Correct answer: C — The vectors are parallel

The magnitude of the cross product |a⃗ × b⃗| = |a⃗||b⃗|sin θ. If the result is zero, then sin θ= 0, which implies θ= 0° (parallel) or θ= 180° (anti-parallel).

Correct answer: B — 0

If two vectors are parallel (or anti-parallel), the angle between them is 0° or 180°. Since sin(0°) = 0 and sin(180°) = 0, the magnitude of their cross product is zero.

Correct answer: A — 0

If the vectors are perpendicular, the angle θ= 90°. Since cos(90°) = 0, the dot product A⃗ · B⃗ = |A⃗| |B⃗| cos(90°) = 0.

Correct answer: D — They are perpendicular to each other.

The dot product of two vectors is defined as A⃗ · B⃗ = |A⃗||B⃗|cos θ, where θ is the angle between them. If A⃗ · B⃗ = 0, then cos θ must be zero, which implies θ= 90°. Therefore, the vectors are perpendicular (orthogonal).

Correct answer: A — Work done

The scalar product of two vectors results in a scalar quantity, which is commonly used to calculate physical quantities like work done (Work = F⃗ · d⃗).

Correct answer: B — Dot product

The dot product of two vectors results in a scalar quantity (a single number), whereas the cross product results in a vector quantity.

Correct answer: D — |a⃗||b⃗|

If a⃗ and b⃗ are parallel, the angle between them is 0° or 180°. The dot product is |a⃗||b⃗|cos(0°) = |a⃗||b⃗| or |a⃗||b⃗|cos(180°) = -|a⃗||b⃗|. Since the question asks for the property related to parallelism, the maximum value, |a⃗||b⃗|, is the defining feature for parallel vectors.

Correct answer: B — They are perpendicular

The definition of the dot product is A⃗ · B⃗ = |A⃗| |B⃗| cos θ. If A⃗ · B⃗ = 0, then cos θ= 0, which means the angle θ between the vectors is 90°. Thus, the vectors are perpendicular (orthogonal).

Correct answer: B — 5

Revisiting the calculation: 5 = 2 · |B⃗| · (1/2), which simplifies to 5 = |B⃗|. Option C is 5.

Correct answer: A — 0⃗

The cross product of two parallel vectors is always zero. The cross product measures the area of the parallelogram, which is zero if the vectors are parallel.