Given A = 1.4𝑎𝑦 and B = -6.9𝑎𝑧, determine |B x A|. (Round your answers to 4 decimal places.)
Question
Given A = 1.4𝑎𝑦 and B = -6.9𝑎𝑧, determine |B x A|. (Round your answers to 4 decimal places.)
Solution 1
The cross product of two vectors A and B is given by the formula:
A x B = |A||B|sin(θ)
where |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.
In this case, A and B are perpendicular to each other (since one is in the y direction and the other is in the z direction), so the angle between them is 90 degrees. The sine of 90 degrees is 1.
The magnitudes of A and B are given as 1.4 and 6.9 respectively.
So, |B x A| = |A||B|sin(θ) = 1.4 * 6.9 * 1 = 9.66
Therefore, |B x A| = 9.66 (rounded to 4 decimal places).
Solution 2
The cross product of two vectors A and B is given by the formula:
A x B = |A||B|sin(θ)
where |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.
In this case, A and B are perpendicular to each other (since one is in the y direction and the other is in the z direction), so the angle between them is 90 degrees. The sine of 90 degrees is 1.
The magnitude of a vector A = 1.4ay is |A| = 1.4. The magnitude of a vector B = -6.9az is |B| = 6.9.
So, |B x A| = |A||B|sin(90) = 1.4 * 6.9 * 1 = 9.66.
Therefore, |B x A| = 9.66.
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