If p¯, q¯ and r¯ are three unit vectors represented by the three sides of an equilateral triangle such that p¯⋅q¯$$+q$$¯. r¯$$=0$$, then which of the following is the correct relation between the three vectors?

Correct option is 2q¯+ r¯=p¯

Questions

If $\bar{p}, \bar{q} and \bar{r}$ are three unit vectors represented by the three sides of an equilateral triangle such that $\bar{p} \cdot \bar{q} + \bar{q} . \bar{r} = 0$ , then which of the following is the correct relation between the three vectors?

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p¯+q¯ = r¯

q¯+ r¯=p¯

r¯+p¯=q¯

p¯+q¯ + r¯=0

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detailed solution

Correct option is B

p¯⋅q¯+q¯. r¯=0 suggests that p¯⋅q¯=−q¯. r¯, so if the angle between left side pair is 60°, then the angle between the right side pair must be 120°.

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If p¯, q¯ and r¯ are three unit vectors represented by the three sides of an equilateral triangle such that p¯⋅q¯+q¯. r¯=0, then which of the following is the correct relation between the three vectors?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If $\bar{p}, \bar{q} and \bar{r}$ are three unit vectors represented by the three sides of an equilateral triangle such that $\bar{p} \cdot \bar{q} + \bar{q} . \bar{r} = 0$ , then which of the following is the correct relation between the three vectors?