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1 Unit 1: Pure Mathematics A

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Question 296

The points AAA, BBB, C C\,C and D D\,D have position vectors a=(13)\mathbf{a} = \begin{pmatrix} 1 \\ 3 \end{pmatrix}a=(13​), b=(36)\mathbf{b} = \begin{pmatrix} 3 \\ 6 \end{pmatrix}b=(36​), c=(75)\mathbf{c} = \begin{pmatrix} 7 \\ 5 \end{pmatrix}c=(75​), d=(5k)\mathbf{d} = \begin{pmatrix} 5 \\ k \end{pmatrix}d=(5k​)

a.

Find the value of k k\,k for which D D\,D is the midpoint of BCBCBC.

[1]
b.

Find the two values of k k\,k for which ∣AD⃗∣=25\left|\vec{AD}\right| = 2\sqrt{5}​AD​=25​.

[3]
c.

Find the value of k k\,k for which ABCD ABCD\,ABCD is a parallelogram.

[2]
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1 Unit 1: Pure Mathematics A Questions

  1. A Level
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