Vector Properties | DP IB Maths: AA HL Topic Questions 2021

1a

3 marks

Given $|a| = 5, b = (\begin{matrix} 12 \\ - 5 \end{matrix})$ and $a \cdot b = 16$ , find the angle between $a$ and $b$ .

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1b

3 marks

Consider a third vector c, where $|c| = 8$ .

When the angle between $a$ and $c$ is $\frac{π}{4}$ , show that $|a \cdot (b + c)| = 16 + 20 \sqrt{2}$ .

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1a

3 marks

Show that the vectors $a = 2 i - 6 j + k$ and $b = - i + 3 j - k$ are not parallel.

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1b

3 marks

Show that $| a \cdot b | < | a | | b |$

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1c

2 marks

Show that $a \cdot a = | a |^{2}$

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1a

4 marks

Given $|a| = 6, |b| = 2$ and $a \times b = (\begin{matrix} - 5 \\ 2 \\ 7 \end{matrix})$ , find the possible values of $a \cdot b$ .

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1b

3 marks

Consider a third vector c, where $|c| = 5 .$

Given that the angle between $a$ and $c$ is $\frac{π}{3}$ , find $|a \times (b + c)|$ .

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DP IB Maths: AA HL