The angle between two unit vectors q and b is $ heta$ and $|a + b| < 1$ - HSC - SSCE Mathematics Extension 1 - Question 6 - 2022 - Paper 1
Question 6
The angle between two unit vectors q and b is $ heta$ and $|a + b| < 1$.
Which of the following best describes the possible range of values of $ heta$?
A. $0 \, \l... show full transcript
Worked Solution & Example Answer:The angle between two unit vectors q and b is $ heta$ and $|a + b| < 1$ - HSC - SSCE Mathematics Extension 1 - Question 6 - 2022 - Paper 1
Step 1
Evaluate the Condition $|a + b| < 1$
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Answer
The inequality ∣a+b∣<1 implies that the vectors a and b cannot be in opposite directions that would create an angle of 180exto. Thus, the maximum angle allowed between them is less than 180exto.
Step 2
Determine the Range of $ heta$
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Answer
Since both vectors are unit vectors, the angle between them, heta, must remain less than rac{2eta}{3} in order to satisfy the inequality. As a result, the possible range of values for heta is as follows: 0 < heta < 2 rac{eta}{3}.
Step 3
Select the Correct Answer
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Answer
The option that best describes this range of values is B. 0 < heta < 2 rac{eta}{3}.
