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Two forces F⃗...

Question

Two forces $_{1} = 5^i + 10^j - 20^k$ and $_{2} = 10^i - 5^j - 15^k$ act on a single point. The angle between $_{1}$ and $_{2}$ (in degree) is nearly

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Solution

Given,
$_{1} = 5^i + 10^j - 20^k$
$_{2} = 10^i - 5^j - 15^k$
$cos θ = \frac{_{1} ._{2}}{| F_{1} | | F_{2} |}$
$= \frac{(5^i + 10^j - 20^k) . (10^i - 5^j - 15^k)}{\sqrt{25 + 100 + 400} \sqrt{100 + 25 + 225}}$
$= \frac{50 - 50 + 300}{\sqrt{525} \sqrt{350}}$

Final Answer: $(45)$

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