Question

find the magnitude of a-b , if vector a * vector b = 8 and magnitude of vector a = 2 , magnitude of vector b = 5

Answer 1

$$\begin{gathered} Given\overrightarrow{a}\times \overrightarrow{b}=8,a=2andb=5 \\ But\overrightarrow{a}\times \overrightarrow{b}=\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\sin \theta \\ So8=2\times 5sin\theta \\ orsin\theta =\frac{4}{5} \\ or\theta =53.2° \\ Now\left|\overrightarrow{a}-\overrightarrow{b}\right|=\sqrt{a^2+b^2-2\times ab\cos 53.2}=\sqrt{4+25-20\times 0.336} \\ \left|\overrightarrow{a}-\overrightarrow{b}\right|=\sqrt{29-6.72}=\sqrt{3.28}=1.8 \end{gathered}$$