The angle between two vectors given by 6i¯+6j¯−3k¯ and 7i¯+4j¯+4k¯ is

The angle between two vectors given by $6 \bar{i} + 6 \bar{j} - 3 \bar{k}$ and $7 \bar{i} + 4 \bar{j} + 4 \bar{k}$ is

A
$\cos^{- 1} (\frac{1}{\sqrt{3}})$
B
$\cos^{- 1} (\frac{5}{\sqrt{3}})$
C
$\sin^{- 1} (\frac{2}{\sqrt{3}})$
D
$\sin^{- 1} (\frac{\sqrt{5}}{3})$

Solution:

If the angle between the vectors is ‘ $θ$ ’ then

$\cos θ = \frac{\vec{A} . \vec{B}}{| \vec{A} | . | \vec{B} |}$

$\Rightarrow \cos θ = \frac{42 + 24 - 12}{(\sqrt{36 + 36 + 9}) (\sqrt{49 + 16 + 16})}$

$\cos θ = \frac{54}{(9) (9)} = \frac{2}{3}$

$∴ \sin θ = \frac{\sqrt{5}}{3}$

$\Rightarrow θ = \sin^{- 1} (\frac{\sqrt{5}}{3})$

Related content

25+ Paulo Coelho Quotes from The Alchemist | Inspirational & Life-Changing

Difference between Its and It’s

National Maritime Day 2025 (5th April), Theme & History

LKG GK Questions and Answers for Kids

Use of Has and Have in a Sentence | English Grammar Rules, Difference & Examples

List of all Input and Output Devices – Definition & Examples

Telugu Year Names | తెలుగు సంవత్సరాల పేర్లు

Murugan Quotes in Tamil | முருகன் மேற்கோள்கள் தமிழில்

100+ Heartfelt Happy Birthday Wishes in Marathi | Messages & Quotes

55 Best Motivational Quotes in Kannada & English for Success