. Calculate the vector product of a and b given thata= 2i + j + k and b = i – j – k ​

Answer:

3[tex]\documentclass{}\begin{document} $$\hat{j} $$\end{document}[/tex] - 3[tex]\documentclass{}\begin{document} $$\hat{k} $$\end{document}[/tex]

Explanation:

Given

A = 2i + j + k

B = i - j - k

To find

Cross-Product of two vectors

To find the cross-product, we use the matrix method to get our answer quickly and accurately.

Representing the values given in the matrix format,

        [tex]\left[\begin{array}{ccc}i&j&k\\2&1&1\\1&-1&-1\end{array}\right][/tex]

[tex]\documentclass{}\begin{document} $$ \vec{A} $$\end{document}[/tex] X [tex]\documentclass{}\begin{document} $$ \vec{B} $$\end{document}[/tex] = [tex]\documentclass{}\begin{document} $$\hat{i} $$\end{document}[/tex] ( 1 x -1 - (1 x -1)) - [tex]\documentclass{}\begin{document} $$\hat{j} $$\end{document}[/tex] (2 x -1 - (1 x 1)) + [tex]\documentclass{}\begin{document} $$\hat{k} $$\end{document}[/tex] (2 x -1 - (1 x 1))

[tex]\documentclass{}\begin{document} $$ \vec{A} $$\end{document}[/tex] X [tex]\documentclass{}\begin{document} $$ \vec{B} $$\end{document}[/tex] = [tex]\documentclass{}\begin{document} $$\hat{i} $$\end{document}[/tex] (-1 + 1) - [tex]\documentclass{}\begin{document} $$\hat{j} $$\end{document}[/tex] ( -2 - 1) + [tex]\documentclass{}\begin{document} $$\hat{k} $$\end{document}[/tex] (-2 -1)

[tex]\documentclass{}\begin{document} $$ \vec{A} $$\end{document}[/tex] X [tex]\documentclass{}\begin{document} $$ \vec{B} $$\end{document}[/tex] = [tex]\documentclass{}\begin{document} $$\hat{i} $$\end{document}[/tex](0) + 3[tex]\documentclass{}\begin{document} $$\hat{j} $$\end{document}[/tex] -3[tex]\documentclass{}\begin{document} $$\hat{k} $$\end{document}[/tex]

[tex]\documentclass{}\begin{document} $$ \vec{A} $$\end{document}[/tex] X [tex]\documentclass{}\begin{document} $$ \vec{B} $$\end{document}[/tex] = 3[tex]\documentclass{}\begin{document} $$\hat{j} $$\end{document}[/tex] - 3[tex]\documentclass{}\begin{document} $$\hat{k} $$\end{document}[/tex]