Final answer:
To find the value of |a x b|, we calculate the cross product of vectors a and b using the formula |a x b| = |a| x |b| x sin(theta). Given |a| = 10, |b| = 2, and a dot b = 12, we solve for cos(theta) and sin(theta). The final result is |a x b| = 16.
Step-by-step explanation:
To find the value of |a x b|, we first need to calculate the cross product of vectors a and b.
The magnitude of the cross product is equal to the product of the magnitudes of the vectors multiplied by the sine of the angle between them.
In this case, |a x b| = |a| x |b| x sin(theta), where theta is the angle between a and b.
Given that |a| = 10, |b| = 2, and a dot b = 12, we can use the formula for the cross product to solve for theta. a dot b = |a| x |b| x cos(theta), which gives us 12 = 10 x 2 x cos(theta).
From this equation, we can solve for cos(theta) by dividing both sides by 20: cos(theta) = 12/20 = 0.6.
Since a and b are both positive, theta must be between 0 and 90 degrees,
which means cos(theta) is positive.
Therefore, sin(theta) = sqrt(1 - cos^2(theta))
= sqrt(1 - 0.6^2)
= sqrt(1 - 0.36)
= sqrt(0.64)
= 0.8.
Finally, we can calculate |a x b| = |a| x |b| x sin(theta)
= 10 x 2 x 0.8
= 16.