Assessment Answers - Integral Maths Vectors Topic

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 ).

( \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.

Hi everyone,

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 ).

( \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.

Hi everyone,

Our use of cookies

We use necessary cookies to make our site work. We'd also like to set optional analytics cookies to help us improve it. We won't set optional cookies unless you enable them. Using this tool will set a cookie on, your device to remember your preferences.

Necessary cookies enable core functionality such as security, network management, and accessibility. You may disable these by changing your browser settings, but this may affect how the website functions. integral maths vectors topic assessment answers

We'd like to set Google Analytics cookies to help us to improve our website by collecting and reporting information on how you use it. The cookies collect information in a way that does not directly identify anyone. Direction vector ( \overrightarrowAB = \beginpmatrix 3 \

I accept all cookies
)