Problem Solving using Vectors (Edexcel A-Level Mathematics): Quizzes

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Problem Solving using Vectors
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In parallelogram ABCDABCD, which vector relationship must be true?

BC→=AD→\overrightarrow{BC} = \overrightarrow{AD}

Convert 6i6i to column vector form.

(60)\begin{pmatrix} 6 \\ 0 \end{pmatrix}

If A=(21)A = \begin{pmatrix} 2 \\ 1 \end{pmatrix} and B=(60)B = \begin{pmatrix} 6 \\ 0 \end{pmatrix}, what is AB→\overrightarrow{AB}?

(4−1)\begin{pmatrix} 4 \\ -1 \end{pmatrix}

Which vectors are parallel to (21)\begin{pmatrix} 2 \\ 1 \end{pmatrix}?

(42)\begin{pmatrix} 4 \\ 2 \end{pmatrix} & (−1−12)\begin{pmatrix} -1 \\ -\frac{1}{2} \end{pmatrix}

What defines a parallelogram using vectors?

Two pairs of parallel sides

What is the vector definition of a rhombus?

Four sides of the same length

To prove ABCDABCD is a parallelogram, what must be shown?

AB→=CD→\overrightarrow{AB} = \overrightarrow{CD} and BC→=AD→\overrightarrow{BC} = \overrightarrow{AD}

Lines with gradients 1 and −14-\frac{1}{4} are perpendicular. True or false?

False, as 1×−14≠−11 \times -\frac{1}{4} \neq -1

Point DD has position vector (0−1)\begin{pmatrix} 0 \\ -1 \end{pmatrix}. What are its coordinates?

(0,−1)(0, -1)

What defines a rectangle using vectors?

Two pairs of parallel sides and right angles

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