SATHEE: Vectors 4 Question 9

Vectors 4 Question 9

9. If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar unit vectors such that $\vec{a} \times (\vec{b} \times \vec{c}) = \frac{(\vec{b} + \vec{c})}{\sqrt{2}}$ , then the angle between $\vec{a}$ and $\vec{b}$ is

(1995, 2M)

(a) $\frac{3 π}{4}$

(b) $\frac{π}{4}$

(d) $π$

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Answer:

Correct Answer: 9. (a)

Solution:

Since, $\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\vec{b} + \vec{c}}{\sqrt{2}}$

$\Rightarrow (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{c} = \frac{1}{\sqrt{2}} \vec{b} + \frac{1}{\sqrt{2}} \vec{c}$

On equating the coefficient of $\vec{c}$ , we get

$\begin{aligned} \vec{a} \cdot \vec{b} & = - \frac{1}{\sqrt{2}} \\ \Rightarrow | \vec{a} | | \vec{b} | \cos θ & = - \frac{1}{\sqrt{2}} \\ ∴ \cos θ & = - \frac{1}{\sqrt{2}} \Rightarrow θ = \frac{3 π}{4} \end{aligned}$

Vectors 4 Question 9

9. If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar unit vectors such that $\vec{a} \times (\vec{b} \times \vec{c}) = \frac{(\vec{b} + \vec{c})}{\sqrt{2}}$ , then the angle between $\vec{a}$ and $\vec{b}$ is

Answer:

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Vectors 4 Question 9

9. If a→,b→,c→ are non-coplanar unit vectors such that a→×(b→×c→)=(b→+c→)2, then the angle between a→ and b→ is

Answer:

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9. If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar unit vectors such that $\vec{a} \times (\vec{b} \times \vec{c}) = \frac{(\vec{b} + \vec{c})}{\sqrt{2}}$ , then the angle between $\vec{a}$ and $\vec{b}$ is