SATHEE: Kinematics Question 590

Kinematics Question 590

Question: Let $\vec{a}$ and $\vec{b}$ be two unit vectors. If the vectors $\vec{c} = \hat{a} + 2 \hat{b}$ and $\vec{d} = 5 \hat{a} - 2 \hat{b}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ it’s:

Options:

A) $\frac{π}{6}$

B) $\frac{π}{2}$

C) $\frac{π}{3}$

D) $\frac{π}{4}$

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Let $\vec{c} = \hat{a} + 2 \hat{b}$ and $\vec{d} = 5 \hat{a} - 4 \hat{b}$

Since $\vec{c}$ and $\vec{d}$ are perpendicular to each other

$∴ \vec{c} . \vec{d} = 0 \Rightarrow (\hat{a} + 2 \hat{b}) . (5 \hat{a} - 4 \hat{b}) = 0$ $\Rightarrow 5 + 6 \hat{a} . \hat{b} - 8 = 0$

$(∴ \vec{a} . \vec{a} = 1)$ $\Rightarrow \hat{a} . \hat{b} = \frac{1}{2} \Rightarrow θ = \frac{π}{3}$

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Kinematics Question 590

Question: Let a→ and b→ be two unit vectors. If the vectors c→=a^+2b^ and d→=5a^−2b^ are perpendicular to each other, then the angle between a^ and b^ it’s:

Options:

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Question: Let $\vec{a}$ and $\vec{b}$ be two unit vectors. If the vectors $\vec{c} = \hat{a} + 2 \hat{b}$ and $\vec{d} = 5 \hat{a} - 2 \hat{b}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ it’s: