The magnitudes of the two vectors 𝐚 and 𝐛 are a and b, respectively. The vector product of a and

Name: Problem 40, Chapter 3: Master Resource Book in JEE Main Physics
Uploaded: 2022-01-22T03:40:56-08:00
Duration: 1 min 51 s
Channel: Dheeraj Sharma
Description: The magnitudes of the two vectors 𝐚 and 𝐛 are a and b, respectively. The vector product of a and 𝐛 cannot be (a) equal to zero (b) less than a b (c) equal to a b (d) greater than a b

step 1 In this question we have given that the magnitude of the two vectors A and B are A and B respect

Question

The magnitudes of the two vectors $\mathbf{a}$ and $\mathbf{b}$ are $a$ and $b$, respectively. The vector product of a and $\mathbf{b}$ cannot be (a) equal to zero (b) less than $a b$ (c) equal to $a b$ (d) greater than $a b$

   The magnitudes of the two vectors $\mathbf{a}$ and $\mathbf{b}$ are $a$ and $b$, respectively. The vector product of a and $\mathbf{b}$ cannot be
(a) equal to zero
(b) less than $a b$
(c) equal to $a b$
(d) greater than $a b$

Master Resource Book in JEE Main Physics

D. B. Singh 1st Edition

Chapter 3, Problem 40

Instant Answer

Solved by Expert Dheeraj Sharma

01/22/2022

Step 1

Step 1: The vector product of two vectors $\mathbf{a}$ and $\mathbf{b}$ is given by $\mathbf{a} \times \mathbf{b} = |\mathbf{a}||\mathbf{b}|\sin\theta \mathbf{n}$, where $\theta$ is the angle between $\mathbf{a}$ and $\mathbf{b}$, and $\mathbf{n}$ is the unit Show more…

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The magnitudes of the two vectors $\mathbf{a}$ and $\mathbf{b}$ are $a$ and $b$, respectively. The vector product of a and $\mathbf{b}$ cannot be (a) equal to zero (b) less than $a b$ (c) equal to $a b$ (d) greater than $a b$

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Key Concepts

Vector Cross Product

The vector cross product of two vectors is another vector that is perpendicular to the plane of the original vectors. Its magnitude is given by the product of the magnitudes of the two vectors and the sine of the angle between them. This formula, a · b · sin(?), demonstrates that the cross product not only depends on the relative sizes of vectors but also on their orientation relative to each other.

Range of the Cross Product Magnitude

Since the sine of any angle lies between 0 and 1, the magnitude of the cross product ranges from zero to the product of the magnitudes of the two vectors. This means that the cross product can be zero if the vectors are parallel or one of them is zero in magnitude, it can be equal to the absolute product only when the vectors are perpendicular, and it cannot exceed the product of the magnitudes of the two vectors.

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