The angle between 𝐀 ×𝐁 and 𝐀+𝐁 is : (a) 90^∘ (b) 180^∘ (c) 60^∘ (d) none of these

Name: Problem 6, Chapter 2: Arihant AIEEE Physics
Uploaded: 2021-09-18T17:28:47-08:00
Duration: 2 min 6 s
Channel: Dheeraj Sharma
Description: The angle between 𝐀 ×𝐁 and 𝐀+𝐁 is : (a) 90^∘ (b) 180^∘ (c) 60^∘ (d) none of these

step 1 In this question we have to find the angle between two vectors that is vector a cross B and vect

The angle between 𝐀 ×𝐁 and 𝐀+𝐁 is : (a) 90^∘ (b) 180^∘ (c)...

The angle between $\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}$ and $\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}$ is :
(a) $90^{\circ}$
(b) $180^{\circ}$
(c) $60^{\circ}$
(d) none of these

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Key Concepts

Cross Product

The cross product of two vectors in three-dimensional space produces a new vector that is perpendicular to the plane containing the original vectors. Its magnitude is given by the product of the magnitudes of the original vectors multiplied by the sine of the angle between them, which makes it particularly useful for finding a normal vector to the plane defined by the inputs.

Vector Orthogonality

Orthogonality refers to the property of two vectors being at a 90-degree angle to each other. In vector analysis, when the dot product of two vectors is zero, it indicates that the vectors are perpendicular. This concept is critical in many applications, including determining the relationship between a cross product (which is inherently orthogonal to its components) and vectors lying in the original plane.

Vector Addition

Vector addition involves combining two or more vectors to form a resultant vector. When summing two vectors, the resultant typically lies in the same plane as the original vectors. This concept helps in understanding the spatial relationship between the resultant vector from vector addition and other vectors, such as a vector produced by a cross product.

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