Final answer:
To find the vector that satisfies the equation 10u - v x = 7xw, calculate the cross product of vectors v and x. Substitute the values in the given equation and solve for u. The vector that satisfies the equation is u = (-1.9, 0.7).
Step-by-step explanation:
To find the vector that satisfies the equation 10u - v x = 7xw, we need to first calculate the cross product of vectors v and x.
Let's find v x:
- v = (-1, -3)
- x = (-5, 1)
- Using the formula for the cross product: v x = (-3)(-5) - (-1)(1) = 15 - (-1) = 16
Now, substitute the values in the given equation:
- 10u - 16 = 7(-5,1)
- 10u - 16 = (-35, 7)
- Adding 16 to both sides: 10u = (-35, 7) + 16
- 10u = (-35+16, 7)
- 10u = (-19, 7)
- Dividing both sides by 10: u = (-1.9, 0.7)
Therefore, the vector that satisfies the equation 10u - v x = 7xw is u = (-1.9, 0.7).