If vector |a| = 12 cm, |b| = 13 cm, and the angle between them when placed tail to tail is 35°, find |a × b| to the nearest centimetre.
.... and no need for placing them head to tail by the way.
To find the magnitude of the cross product between vectors |a| and |b|, we can use the formula:
|a × b| = |a| |b| sin(θ)
where |a| is the magnitude of vector |a|, |b| is the magnitude of vector |b|, and θ is the angle between them.
Given that |a| = 12 cm, |b| = 13 cm, and the angle between them is 35°, we can substitute these values into the formula:
|a × b| = 12 cm * 13 cm * sin(35°)
Using a scientific calculator, we can calculate the value of sin(35°) which is approximately 0.5736. Plugging this value into the formula, we get:
|a × b| ≈ 12 cm * 13 cm * 0.5736
Simplifying the expression, we have:
|a × b| ≈ 88.3872 cm²
Rounding this value to the nearest centimeter, we get:
|a × b| ≈ 88 cm
Therefore, the magnitude of the cross product |a × b| is approximately 88 cm.
To find the magnitude of the cross product |a × b|, we can use the formula:
|a × b| = |a| * |b| * sin(θ)
where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.
Given that |a| = 12 cm, |b| = 13 cm, and the angle between them is 35°, we can plug these values into the formula and calculate the magnitude of the cross product:
|a × b| = 12 cm * 13 cm * sin(35°)
To evaluate sin(35°), you can use a scientific calculator or reference a trigonometric table. In this case, sin(35°) is approximately 0.574.
Substituting this value back into the formula, we have:
|a × b| = 12 cm * 13 cm * 0.574
|a × b| ≈ 89.352 cm
Rounding to the nearest centimeter, the magnitude of |a × b| is approximately 89 cm.
|a × b| = |a| * |b| * sinθ
just plug in your numbers!