Integral Maths Vectors Topic Assessment Answers Apr 2026

I’ve outlined the key steps. Question 1 – Vector magnitude and unit vectors Typical Q: Find ( |\mathbfa| ) given ( \mathbfa = 4\mathbfi - 3\mathbfj + 2\mathbfk ).

( \mathbfa \cdot \mathbfb = 2(1) + k(-2) + 3(4) = 2 - 2k + 12 = 14 - 2k = 0 ) ( 2k = 14 \Rightarrow k = 7 ). Quick Answer Summary (for checking) | Q# | Topic | Answer | |----|----------------------|--------------------------------| | 1 | Magnitude & unit vector | ( \sqrt29 ), ( \frac1\sqrt29(4,-3,2) ) | | 2 | Dot product / angle | ( \approx 94.8^\circ ) | | 3 | Line equation | ( (2,-1,3) + \lambda(3,2,-3) ) | | 4 | Intersection | Skew lines (no intersection) | | 5 | Perpendicular vectors | ( k = 7 ) | Note: Integral Maths changes the numbers slightly for different students sometimes. If your numbers differ, follow the same method – the structure is identical.

Lines are skew (no intersection). Check your given numbers carefully – mine showed no solution. Question 5 – Perpendicular vectors & constant finding Typical Q: ( \mathbfa = \beginpmatrix 2 \ k \ 3 \endpmatrix ), ( \mathbfb = \beginpmatrix 1 \ -2 \ 4 \endpmatrix ) are perpendicular. Find ( k ). integral maths vectors topic assessment answers

Direction vector ( \overrightarrowAB = \beginpmatrix 3 \ 2 \ -3 \endpmatrix ) Equation: ( \mathbfr = \beginpmatrix 2 \ -1 \ 3 \endpmatrix + \lambda \beginpmatrix 3 \ 2 \ -3 \endpmatrix ), ( \lambda \in \mathbbR ). Question 4 – Intersection of two lines Typical Q: ( L_1: \mathbfr = \beginpmatrix 1 \ 0 \ 2 \endpmatrix + s\beginpmatrix 2 \ -1 \ 1 \endpmatrix ), ( L_2: \mathbfr = \beginpmatrix 4 \ 2 \ 1 \endpmatrix + t\beginpmatrix 1 \ 1 \ -2 \endpmatrix ).

Integral Maths Vectors Topic Assessment – Worked Answers & Solutions I’ve outlined the key steps

Let me know if you want me to post the full handwritten working for any question!

scroll to the summary table at the bottom. Quick Answer Summary (for checking) | Q# |

Unit vector = ( \frac1\sqrt29(4\mathbfi - 3\mathbfj + 2\mathbfk) ). Typical Q: Given ( \mathbfp = \beginpmatrix 1 \ 2 \ -1 \endpmatrix ), ( \mathbfq = \beginpmatrix 3 \ 0 \ 4 \endpmatrix ), find the angle between them.

I’ve just finished the topic assessment on Integral Maths (Edexcel A-Level Maths / Core Pure) and wanted to share my worked answers. Please double-check these as mistakes do happen!

( \sqrt4^2 + (-3)^2 + 2^2 = \sqrt16 + 9 + 4 = \sqrt29 )

Hi everyone,