Unit vector in given direction

Find a unit vector in the direction of a given vector by dividing the vector by its magnitude.

4 questions · Moderate -1.0

1.10c Magnitude and direction: of vectors
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OCR C4 2011 June Q2
3 marks Easy -1.2
2 Find the unit vector in the direction of \(\left( \begin{array} { c } 2 \\ - 3 \\ \sqrt { 12 } \end{array} \right)\).
CAIE P1 2012 June Q2
5 marks Moderate -0.8
Relative to an origin \(O\), the position vectors of the points \(A\), \(B\) and \(C\) are given by $$\overrightarrow{OA} = \begin{pmatrix} 2 \\ -1 \\ 4 \end{pmatrix}, \quad \overrightarrow{OB} = \begin{pmatrix} 4 \\ 2 \\ -2 \end{pmatrix} \quad \text{and} \quad \overrightarrow{OC} = \begin{pmatrix} 1 \\ 3 \\ p \end{pmatrix}.$$ Find
  1. the unit vector in the direction of \(\overrightarrow{AB}\), [3]
  2. the value of the constant \(p\) for which angle \(BOC = 90°\). [2]
AQA AS Paper 1 Specimen Q13
2 marks Easy -1.2
  1. The unit vectors \(\mathbf{i}\) and \(\mathbf{j}\) are perpendicular. Find the magnitude of the vector \(-20\mathbf{i} + 21\mathbf{j}\) Circle your answer. [1 mark] \(-1\) \(1\) \(\sqrt{41}\) \(29\)
  2. The angle between the vector \(\mathbf{i}\) and the vector \(-20\mathbf{i} + 21\mathbf{j}\) is \(\theta\) Which statement about \(\theta\) is true? Circle your answer. [1 mark] \(0° < \theta < 45°\) \(45° < \theta < 90°\) \(90° < \theta < 135°\) \(135° < \theta < 180°\)
Edexcel AS Paper 1 Q3
5 marks Moderate -0.8
Given that the point \(A\) has position vector \(x\mathbf{i} - \mathbf{j}\), the point \(B\) has position vector \(-2\mathbf{i} + y\mathbf{j}\) and \(\overrightarrow{AB} = -3\mathbf{i} + 4\mathbf{j}\), find
  1. the values of \(x\) and \(y\) [3]
  2. a unit vector in the direction of \(\overrightarrow{AB}\). [2]