[Solved] Let a=2i+3j+4k and b=3i+4j+5k . Find the angle between them. - Concepts of Physics

We have:a=2i+3j+4kb=3i+4j+5kUsing scalar product, we can find the angle between vectors b=3i+4j+5k and a.i.e.,bSo, a.b=∣a∣∣∣b∣∣cosθ=cos−1((22+32+42)(32+42+52)2×3+3×4+4×5)θ=cos−1(∣a∣∣b∣a.b)∴ The required angle is =cos−1((22+32+42)(32+42+52)2×3+3×4+4×5)

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Let {a} = 2 {i} + 3 {j} + 4 {k} { and } {b} = 3 {i} + 4 {j} +

Concepts of Physics

Class 11

HC Verma Part I

Chapter 1: Introduction to Physics

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Chapter 2: Physics and Mathematics

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Let

A_{1} A_{2} A_{3} A_{4} A_{5} A_{6} A_{1}

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Let

a = 2 i + 3 j + 4 k and b = 3 i + 4 j + 5 k

. Find the angle between them.

Prove that

A . (A \times B) = 0

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Question

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Solving time: 5 mins

Let $a = 2 i + 3 j + 4 k and b = 3 i + 4 j + 5 k$ . Find the angle between them.

Views: 6,351 students

Updated on: Sep 24, 2022

Book:

Concepts of Physics (HC Verma Part I)

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a = 2 i + 3 j + 4 k and b = 3 i + 4 j + 5 k

. Find the angle between them.

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Text solutionVerified

We have:

a = 2 i + 3 j + 4 k

b = 3 i + 4 j + 5 k

Using scalar product, we can find the angle between vectors

b = 3 i + 4 j + 5 k

and

a

.i.e.,

b

So,

a . b = ∣ a ∣ ∣ ∣ b ∣ ∣ cos θ

= cos^{- 1} (\frac{2 \times 3 + 3 \times 4 + 4 \times 5}{( 2 ^{2} + 3 ^{2} + 4 ^{2} ) ( 3 ^{2} + 4 ^{2} + 5 ^{2} )})

θ = cos^{- 1} (\frac{a . b}{∣ a ∣ ∣ b ∣})

∴ The required angle is

= cos^{- 1} (\frac{2 \times 3 + 3 \times 4 + 4 \times 5}{( 2 ^{2} + 3 ^{2} + 4 ^{2} ) ( 3 ^{2} + 4 ^{2} + 5 ^{2} )})

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Question Text	Let $a = 2 i + 3 j + 4 k and b = 3 i + 4 j + 5 k$ . Find the angle between them.
Updated On	Sep 24, 2022
Topic	Physical World
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 3
Upvotes	660
Avg. Video Duration	5 min

Let $a = 2 i + 3 j + 4 k and b = 3 i + 4 j + 5 k$ . Find the angle between them.

Text solutionVerified

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