Question 92: Motion in 2D & Vectors

Question

$$ \begin{aligned} & 	ext { If }|\vec{a}|=\sqrt{26},|\vec{b}|=7 \ & |\vec{a} 	imes \vec{b}|=35 	ext {, find } \vec{a} \cdot \vec{b} \end{aligned} $$

Accepted Answer

$$ \begin{aligned} & |\vec{a}|=\sqrt{26},|\vec{b}|=7 \ & |\vec{a} 	imes \vec{b}|=35 \ & |\vec{a} 	imes \vec{b}|=|\vec{a}||\vec{b}| \sin 	heta \ & \sin 	heta=\frac{35}{7 \sqrt{26}}=\frac{5}{\sqrt{26}} \ & \begin{aligned} \vec{a} \cdot \vec{b} & =|\vec{a}||\vec{b}| \cos 	heta \ & =\sqrt{26} \cdot 7 \cdot \cos 	heta \end{aligned} \ & \sin 	heta=\frac{5}{\sqrt{26}} \ & \cos 	heta=\sqrt{1-\sin ^2 	heta}=\sqrt{1-\frac{25}{26}}=\sqrt{\frac{1}{26}}=\frac{1}{\sqrt{26}} \ & \vec{a} \cdot \vec{b}=\sqrt{26} \cdot 7 \cdot \frac{1}{\sqrt{26}}=7 \end{aligned} $$

Answer

4

Answer

5

Answer

6

Answer

7

Motion in 2D & Vectors

\begin{aligned} & \text { If }|\vec{a}|=\sqrt{26},|\vec{b}|=7 \\ & |\vec{a} \times \vec{b}|=35 \text {, find } \vec{a} \cdot \vec{b} \end{aligned}

Choose the correct answer: