91影视

The given data can be expressed below as:

• The scalar product of vectors $\stackrel{鈬赌}{\mathrm{A}}\mathrm{and}\stackrel{鈬赌}{\mathrm{B}}\mathrm{is}-6.00.$
• The vector product of vectors $\stackrel{鈬赌}{\mathrm{A}}\mathrm{and}\stackrel{鈬赌}{\mathrm{B}}\mathrm{is}+9.00.$

This scalar or dot product is the algebraic operation that takes 鈥渢wo equal-length鈥� numbers and returns a single piece of number.

The vector or cross product is the two vector鈥檚 binary operation in the 3-D space.

Dividing the magnitude of the scalar and the vector product gives the angle between the two vectors.

The magnitude of the dot product of the vector can be expressed as:

$\stackrel{鈬赌}{A}.\stackrel{鈬赌}{B}=\left|\stackrel{鈬赌}{A}\right|\left|\stackrel{鈬赌}{B}\right|\cos 胃$

Here, $\stackrel{鈬赌}{\mathrm{A}}\mathrm{and}\stackrel{鈬赌}{\mathrm{B}}$are the vectors having the scalar product which is:

role="math" localid="1655791391574" $-6.00=\left|\stackrel{鈬赌}{A}\right|\left|\stackrel{鈬赌}{B}\right|\cos 胃........鈥�\left(1\right)$

The magnitude of the cross product of the vector can be expressed as:

role="math" $\stackrel{鈬赌}{A}脳\overline{B}=\left|\stackrel{鈬赌}{A}\right|\left|\stackrel{鈬赌}{B}\right|\sin 胃$

Here, and are the vectors having the vector product which is:

$+9.00=\left|\stackrel{鈬赌}{A}\right|\left|\stackrel{鈬赌}{B}\right|\sin 胃..........\left(2\right)$

Now, divide equation (2) and (1), which results in,

$$\begin{gathered} \frac{+9.00}{-6.00}=\frac{\left|\stackrel{鈬赌}{A}\right|\left|\stackrel{鈬赌}{B}\right|\sin 胃}{\left|\stackrel{鈬赌}{A}\right|\left|\stackrel{鈬赌}{B}\right|\cos 胃} \\ \tan 胃=\frac{9}{-6} \\ 胃={\tan }^{-1}\left[\frac{9}{-6}\right] \\ 胃=-56.{31}^{掳} \end{gathered}$$

Hence, the angle between two vectors$\stackrel{鈬赌}{\mathrm{A}}\mathrm{and}\stackrel{鈬赌}{\mathrm{B}}\mathrm{is}胃=-56.{31}^{掳}.$