SATHEE: Kinematics Question 30

Kinematics Question 30

Question: Two forces ${\vec{F}}_{1} = 5 \hat{i} + 10 \hat{j} - 20 \hat{k}$ and ${\vec{F}}_{2} = 10 \hat{i} - 5 \hat{j} - 15 \hat{k}$ act on a single point. The angle between ${\vec{F}}_{1}$ and ${\vec{F}}_{2}$ it’s nearly [AMU 1995]

Options:

A) $30^{\circ}$

B) $45^{\circ}$

C) $60^{\circ}$

D) $90^{\circ}$

Show Answer

Answer:

Correct Answer: B

Solution:

$\cos θ = \frac{\vec{F_{1}} . \vec{F_{2}}}{| F_{1} | | F_{2} |}$

$= \frac{(5 \hat{i} + 10 \hat{j} - 20 \hat{k}) . (10 \hat{i} - 5 \hat{j} - 15 \hat{k})}{\sqrt{25 + 100 + 400} \sqrt{100 + 25 + 225}}$

$= \frac{50 - 50 + 300}{\sqrt{525} \sqrt{350}}$
therefore $\cos θ = \frac{1}{\sqrt{2}}$
$∴$ $θ = 45^{\circ}$

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Kinematics Question 30

Question: Two forces F→1=5i^+10j^−20k^ and F→2=10i^−5j^−15k^ act on a single point. The angle between F→1 and F→2 it’s nearly [AMU 1995]

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Question: Two forces ${\vec{F}}_{1} = 5 \hat{i} + 10 \hat{j} - 20 \hat{k}$ and ${\vec{F}}_{2} = 10 \hat{i} - 5 \hat{j} - 15 \hat{k}$ act on a single point. The angle between ${\vec{F}}_{1}$ and ${\vec{F}}_{2}$ it’s nearly [AMU 1995]