With respect to the origin $$\(O\)$$, the points $$\(A\)$$ and $$\(B\)$$ have position vectors given by $$\(\overrightarrow{O A}=\left(\begin{array}{l}1 \\ 2 \\ 1\end{array}\right)\)$$ and $$\(\overrightarrow{O B}=\left(\begin{array}{r}3 \\ 1 \\ -2\end{array}\right)\)$$. The line $$\(l\)$$ has equation $$\(\mathbf{r}=\left(\begin{array}{l}2 \\ 3 \\ 1\end{array}\right)+\lambda\left(\begin{array}{r}1 \\ -2 \\ 1\end{array}\right)\)$$ Find the acute angle between the directions of $$\(A B\)$$ and $$\(l\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_31 Year：2021 Question No：8(a)
Answer:
State or imply \( \overrightarrow{A B}=\left(\begin{array}{c}2 \\ -1 \\ -3\end{array}\right) \)
Use the correct process to calculate the scalar product of a pair of relevant vectors, e.g. their \(\overrightarrow{A B}\) and a direction vector for \(l\)
Using the correct process for the moduli, divide the scalar product by the product of the moduli of the two vectors and evaluate the inverse cosine of the result
Obtain answer \(83.7^{\circ}\) or \(1.46\) radians
Use the correct process to calculate the scalar product of a pair of relevant vectors, e.g. their \(\overrightarrow{A B}\) and a direction vector for \(l\)
Using the correct process for the moduli, divide the scalar product by the product of the moduli of the two vectors and evaluate the inverse cosine of the result
Obtain answer \(83.7^{\circ}\) or \(1.46\) radians
Knowledge points:
3.7.4 understand the significance of all the symbols used when the equation of a straight line is expressed in the form r = a +tb, and find the equation of a line, given sufficient information
3.7.6 use formulae to calculate the scalar product of two vectors, and use scalar products in problems involving lines and points.
Solution:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download