SATHEE: Vectors 1 Question 12

Vectors 1 Question 12

13. If $\vec{a}$ and ${\vec{b}}_{1}$ are two unit vectors such that $\vec{a} + 2 \vec{b}$ and $5 \vec{a} - 4 \vec{b}$ , are perpendicular to each other, then the angle between $\vec{a}$ and $\vec{b}$ is

$(2002, 1 M)$

(a) $45^{\circ}$

(b) $60^{\circ}$

(d) $\cos^{- 1} (\frac{2}{7})$

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Answer:

Correct Answer: 13. (b)

Solution:

Since,

$(\vec{a} + 2 \vec{b}) \cdot (5 \vec{a} - 4 \vec{a}) = 0$

$\begin{aligned} \Rightarrow 5 | \vec{a} |^{2} + 6 \vec{a} \cdot \vec{b} - 8 | \vec{b} |^{2} = 0 \\ \Rightarrow 6 \vec{a} \cdot \vec{b} = 3 [∵ | \vec{a} | = | \vec{b} | = 1] \\ \Rightarrow \cos θ = \frac{1}{2} \Rightarrow θ = 60^{\circ} \end{aligned}$

Vectors 1 Question 12

13. If $\vec{a}$ and ${\vec{b}}_{1}$ are two unit vectors such that $\vec{a} + 2 \vec{b}$ and $5 \vec{a} - 4 \vec{b}$ , are perpendicular to each other, then the angle between $\vec{a}$ and $\vec{b}$ is

Answer:

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Vectors 1 Question 12

13. If a→ and b→1 are two unit vectors such that a→+2b→ and 5a→−4b→, are perpendicular to each other, then the angle between a→ and b→ is

Answer:

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13. If $\vec{a}$ and ${\vec{b}}_{1}$ are two unit vectors such that $\vec{a} + 2 \vec{b}$ and $5 \vec{a} - 4 \vec{b}$ , are perpendicular to each other, then the angle between $\vec{a}$ and $\vec{b}$ is