Quick questions on Vectors: components, magnitude, position vectors and geometry - OCR A-Level Maths A

3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is ratios along a line?

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A point

P

dividing

AB

in the ratio

m : n

has position vector

\mathbf{p} = \mathbf{a} + \dfrac{m}{m + n}(\mathbf{b} - \mathbf{a})

. Setting

m = n

recovers the midpoint formula.

What is q1?

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Find a unit vector in the direction of

6\mathbf{i} + 8\mathbf{j}

. [2 marks]

What is q2?

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Points

A

and

B

have position vectors

\mathbf{i} - 2\mathbf{j} + 3\mathbf{k}

and

4\mathbf{i} + \mathbf{j} - \mathbf{k}

. Find the distance

AB

. [2 marks]

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