Find the angle between the vectors $\bar{a}=3\hat{i} + 4\hat{j}$ and $\bar{b}=6\hat{i}

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Find the angle between the vectors

$\bar{a}=3\hat{i} + 4\hat{j}$ and

$\bar{b}=6\hat{i} - 3\hat{j} + 2\hat{k}$

written 7.2 years ago by

neeta.vanage • 880

modified 3.2 years ago by

pedsangini276 • 4.8k

Subject: Applied Physics 2

Topic: Electrodynamics

Difficulty: Medium

engineering physics

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1 Answer

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written 7.1 years ago by

neeta.vanage • 880

modified 7.1 years ago by

saurabhsingh • 40

$\text {Formula a ⃗.b ⃗ = ab cosθ }$

$(a_1 ) = a_1 i ̂ +a_2 j ̂ +a_3 k ̂ = 3i ̂ +4 j ̂+0\\ a_1=3 ,a_2=4 ,a_3=0 \\$

$(b_1 ) ⃗= b_1 i ̂ +b_2 j ̂ +b_3 k ̂ \\ = 6i ̂ +3j ̂+2k ̂ \\ 〖 b〗_1=6 ,b_2=3,b_3=2 \\$

$a ⃗.b ⃗ = 6 \\ |a ⃗ | = 5 \\ |b ⃗ | = 7 \\$

$\text {Therefore cosθ = (a ⃗.b ⃗)/(|a ⃗ |.|b ⃗ | ) = 6/35 } \\$

$\text{ θ=cos^{-1} 6/35 = 80029 } \\$

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