IB Mathematics Analysis and Approaches Topic AHL…

Let $\vec{a} = 3\vec{i} - \vec{j} + 2\vec{k}$ and .

(a) Find $\vec{a}\cdot\vec{b}$ and .

(b) Find the value of $\lambda$ for which $\vec{a} - \lambda\vec{b}$ is perpendicular to .

(d) Find the exact value of $\cos\theta$ , where $\theta$ is the angle between $\vec{a}$ and $\vec{b}$ .

Consider points $A(1,-3,4)$ , $B(3,-2,6)$ , $C(2,-1,2)$ .

(a) Find $\overrightarrow{AB}$ and $\overrightarrow{AC}$ .

(b) Compute angle $BAC$ . Give your answer in degrees or radians.

(d) Find the distance from $A$ to the line $BC$ .

Let $\vec{u}$ and $\vec{v}$ be vectors with and , and let be the angle between them.

(a) Find expressions for $\left|\vec{u}+\vec{v}\right|^{2}$ and in terms of .

(b) Given that $\left|\vec{u}+\vec{v}\right| = 10$ , find the value of , correct to three significant figures.

(d) Find the two values of $\theta$ for which the angle between $\vec{u}+\vec{v}$ and is radians, each correct to three significant figures.

Find the angle between the vectors $\mathbf{a}=-4\mathbf{i}-2\mathbf{j}$ and $\mathbf{b}=\mathbf{i}-7\mathbf{j}$ , giving your answer in exact form.

IB Mathematics Analysis and Approaches AHL 3.13—scalar (dot) Product Questionbank