Question

If Vector u=(5,-7) and v=(-11,3), 2v-6u=_____ and ||2v-6u||≈_____

Answer 1

The vector resulting from the operation 2v - 6u is (-52, 48). The magnitude of this vector, denoted as ||2v - 6u||, is approximately 70.77.

Step-by-step explanation:

To calculate the vector 2v-6u, we need to multiply vector v by 2, vector u by 6, and then subtract the latter from the former:

• 2v = 2(-11, 3) = (-22, 6)
• 6u = 6(5, -7) = (30, -42)
• 2v - 6u = (-22, 6) - (30, -42) = (-22 - 30, 6 + 42) = (-52, 48)

The resulting vector is (-52, 48).

To find the magnitude of this vector, we use the formula ||a|| = √(ax2 + ay2):

• ||2v - 6u|| = √((-52)2 + (48)2)
• ||2v - 6u|| = √(2704 + 2304)
• ||2v - 6u|| = √5008
• ||2v - 6u|| ≈ 70.77

Approximately, the magnitude is 70.77.