Position Vectors (Edexcel A-Level Mathematics): Quizzes

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Position Vectors
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What does a position vector represent?

Position of a point relative to fixed origin

What is the 2D position vector for point P(5,−3)P(5, -3)?

(5−3)\begin{pmatrix} 5 \\ -3 \end{pmatrix}

What notation is commonly used for the position vector of point PP from origin OO?

r\mathbf{r} or OP\mathbf{OP}

What is the 3D position vector for point Q(1,4,−2)Q(1, 4, -2)?

(14−2)\begin{pmatrix} 1 \\ 4 \\ -2 \end{pmatrix}

If a\mathbf{a} and b\mathbf{b} are position vectors of AA and BB, what is AB\mathbf{AB}?

b−a\mathbf{b} - \mathbf{a}

What is the magnitude of position vector r=(34)\mathbf{r} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}?

55

What is the magnitude of r=(2−12)\mathbf{r} = \begin{pmatrix} 2 \\ -1 \\ 2 \end{pmatrix} in 3D?

33

How is the direction of a position vector found?

By normalizing or using direction cosines

When are three points collinear?

When they lie on the same straight line

If BC→=8×AB→\overrightarrow{BC} = 8 \times \overrightarrow{AB}, what can we conclude about points AA, BB, CC?

They are collinear

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