The magnitude of i.(j×k) is equal to?
Correct answer: B. 1
- A. 0
- B. 1
- C. -1
- D. 2
Explanation
The given expression i.(j×k) is an example of a scalar triple product, which represents the volume of the parallelepiped formed by the vectors i, j, and k. Here, i, j, and k are the standard unit vectors along the x, y, and z axes, respectively. According to the right-hand rule, j×k = i. Therefore, the scalar triple product i.(j×k) simplifies to i.i, which equals 1 since i is a unit vector and the angle between identical vectors is 0 degrees, leading to cos(0) = 1. Thus, the magnitude of the scalar triple product is 1.The incorrect options can be ruled out based on the properties of orthogonal unit vectors:Option A: 0 is incorrect because the vectors are not coplanar.Option C: -1 would only be correct in a left-handed system, which is not applicable here.Option D: 2 is incorrect because the magnitude cannot exceed 1 for unit vectors.
This question appeared on the ETEA MDCAT 2008 paper, which you can sit online with every answer explained.
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About Vector Product
The vector product, or cross product, gives a vector perpendicular to two multiplying vectors, with magnitude AB sin θ and direction set by the right-hand rule. It covers properties such as anti-commutation, area from cross products, torque and angular momentum. Unlike the dot product, its result is a vector.
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