The angle between 𝐀=𝐢̂+𝐣̂ and 𝐁=𝐢̂-𝐣̂ is (a) 45^∘ (b) 90^∘ (c) -45^∘ (d) 180^∘

Name: Problem 17, Chapter 3: Master Resource Book in JEE Main Physics
Uploaded: 2022-01-21T15:29:52-08:00
Duration: 1 min 27 s
Channel: Dheeraj Sharma
Description: The angle between 𝐀=𝐢̂+𝐣̂ and 𝐁=𝐢̂-𝐣̂ is (a) 45^∘ (b) 90^∘ (c) -45^∘ (d) 180^∘

step 1 In this question we have to find the angle between vector A and vector B. So we have given the v

The angle between 𝐀=𝐢̂+𝐣̂ and 𝐁=𝐢̂-𝐣̂ is (a) 45^∘ (b) 90^∘...

Key Concepts

Orthogonality

Orthogonality describes the condition when two vectors are perpendicular to each other. In practice, if the dot product of two non-zero vectors is zero, then the vectors are orthogonal. This concept is widely used in various fields, including linear algebra, physics, and computer graphics.

Vector Magnitude

The magnitude of a vector, also known as its norm or length, is a measure of how long the vector is. It is calculated as the square root of the sum of the squares of its components. Vector magnitude is crucial when normalizing vectors or computing the angle between vectors using the dot product formula.

Angle Between Vectors

The angle between two vectors can be determined using the dot product formula: the dot product equals the product of the vectors' magnitudes and the cosine of the angle between them. By rearranging this formula, the cosine of the angle can be isolated and the angle can be computed, which is essential in understanding the relationship between two vectors.

Vectors

Vectors are mathematical objects characterized by both magnitude and direction. They are often represented in component form and are fundamental in many areas of mathematics and physics, especially when describing quantities like displacement, velocity, and force.

Dot Product

The dot product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number. It is used to determine the angle between two vectors and to project one vector onto another. The dot product of two vectors equals the product of their magnitudes and the cosine of the angle between them.

Transcript

Please give Ace some feedback