The magnitude of cross product of two parallel vectors a and b is equal to:
Correct answer: B. 0
- A. ab cosec θ°
- B. 0
- C. 2ab
- D. abcos θ°
Explanation
The magnitude of the cross product of two parallel vectors a and b is 0. The magnitude of the cross product of two vectors a and b is given by |a x b| = |a| |b| sin θ, where |a| represents the magnitude of vector a, |b| represents the magnitude of vector b, and θ represents the angle between vectors a and b. When the vectors a and b are parallel, the angle between them is either 0° or 180°. In either case, the sine of the angle, sin θ, will be 0. Using the formula, we can see that |a x b| = |a| |b| sin θ = |a| |b| * 0 = 0. Therefore, the magnitude of the cross product of two parallel vectors a and b is indeed 0.
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About Vectors and Equilibrium
Vectors have magnitude and direction, unlike scalars, and are combined by head-to-tail or parallelogram methods. Work covers rectangular components, equilibrium when the resultant force is zero, the scalar product for work and projections, and the vector product for torque and cross-product direction using the right-hand rule.
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