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# Write the value of the product of vectors $\left( {{\text{i}} \times {\text{j}}} \right).{\text{k + }}\left( {{\text{j}} \times {\text{k}}} \right).{\text{i }}$.

Last updated date: 13th Jul 2024
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Hint: The cross product two unit vector is the vector perpendicular to both of them. And, the dot product of two unit vectors in the same direction is equal to 1.

We have , an equation $\left( {{\text{i}} \times {\text{j}}} \right).{\text{k + }}\left( {{\text{j}} \times {\text{k}}} \right).{\text{i }}$. The vectors i, j and k are the vectors in x-direction , y-direction and the z-direction.
There are three operations involved in these expressions.
1) Cross product of two unit vector
2) Dot product of two unit vector
${\text{i}} \to {\text{j}} \to {\text{k}} \to {\text{i}} \\ {\text{i}} \times {\text{j = k}} \\ {\text{j}} \times {\text{k = i}} \\ {\text{k}} \times {\text{i = j}} \\$
$\left( {{\text{i}} \times {\text{j}}} \right).{\text{k + }}\left( {{\text{j}} \times {\text{k}}} \right).{\text{i }}$= k.k + i.i
${\text{a}}{\text{.b = |a||b|cos}}\theta$ where $\theta$ is the angle between vectors a and b.
$\left( {{\text{i}} \times {\text{j}}} \right).{\text{k + }}\left( {{\text{j}} \times {\text{k}}} \right).{\text{i }}$= k.k + i.i
The value of $\left( {{\text{i}} \times {\text{j}}} \right).{\text{k + }}\left( {{\text{j}} \times {\text{k}}} \right).{\text{i }}$is 2.