The Scalar Product (AQA A-Level Further Maths): Quizzes

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The Scalar Product
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What type of quantity does the scalar product of two vectors produce?

A scalar

What is the formula for a⋅b\mathbf{a} \cdot \mathbf{b} in terms of magnitudes and angle?

∣a∣∣b∣cos⁡θ|\mathbf{a}||\mathbf{b}|\cos\theta

What is (2i+3j+k)⋅(i−2j+4k)(2\mathbf{i} + 3\mathbf{j} + \mathbf{k}) \cdot (\mathbf{i} - 2\mathbf{j} + 4\mathbf{k})?

00

What is the value of j⋅k\mathbf{j} \cdot \mathbf{k}?

00

If a⋅b=0\mathbf{a} \cdot \mathbf{b} = 0, what can you conclude about vectors a\mathbf{a} and b\mathbf{b}?

They are perpendicular

Which property does a⋅(b+c)=a⋅b+a⋅c\mathbf{a} \cdot (\mathbf{b} + \mathbf{c}) = \mathbf{a} \cdot \mathbf{b} + \mathbf{a} \cdot \mathbf{c} demonstrate?

Distributive property

Is the scalar product commutative?

Yes, a⋅b=b⋅a\mathbf{a} \cdot \mathbf{b} = \mathbf{b} \cdot \mathbf{a}

What formula finds the angle θ\theta between vectors a\mathbf{a} and b\mathbf{b}?

cos⁡θ=a⋅b∣a∣∣b∣\cos\theta = \frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}||\mathbf{b}|}

How do you find the obtuse angle between two lines from their acute angle?

Subtract the acute angle from 180°

What is ∣a∣|\mathbf{a}| if a=(2−12)\mathbf{a} = \begin{pmatrix} 2 \\ -1 \\ 2 \end{pmatrix}?

33

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