SATHEE: Vectors 2 Question 9

Vectors 2 Question 9

9. Let $\vec{a}, \vec{b}, \vec{c}$ be unit vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ . Which one of the following is correct?

(2007, 3M)

(a) $\vec{a} \times \vec{b} = \vec{b} \times \vec{c} = \vec{c} \times \vec{a} = \vec{0}$

(b) $\vec{a} \times \vec{b} = \vec{b} \times \vec{c} = \vec{c} \times \vec{a} \neq \vec{0}$

(d) $\vec{a} \times \vec{b}, \vec{b} \times \vec{c}, \vec{c} \times \vec{a}$ are mutually perpendicular

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Answer:

Correct Answer: 9. (b)

Solution:

Since, $\vec{a}, \vec{b}, \vec{c}$ are unit vectors and $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ , then

$\vec{a}, \vec{b}, \vec{c}$ represent an equilateral triangle.

$∴ \vec{a} \times \vec{b} = \vec{b} \times \vec{c} = \vec{c} \times \vec{a} \neq \vec{0}$

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Vectors 2 Question 9

9. Let a→,b→,c→ be unit vectors such that a→+b→+c→=0→. Which one of the following is correct?

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9. Let $\vec{a}, \vec{b}, \vec{c}$ be unit vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ . Which one of the following is correct?