Question

If v and w are two vectors of magnitudes 6 and 9/2​ respectively, and the angle between them is 121∘, find ∥​2w−1/3​v∥​. If necessary, round your answer to the nearest tenth.

Answer 1

To find the magnitude of 2w - (1/3)v, we need to find the individual magnitudes of w and v and apply the properties of vector addition and scalar multiplication.

Step-by-step explanation:

To find the magnitude of 2w - (1/3)v, we need to find the individual magnitudes of w and v and apply the properties of vector addition and scalar multiplication. The magnitude of a vector is the square root of the sum of its components squared. So, we can start by finding the magnitude of w, which is given to be 9/2. Next, we find the magnitude of v to be 6. Now, we can find the magnitude of 2w - (1/3)v by substituting the values and performing the calculations.

Let's calculate:

1. Find the magnitude of w: 9/2
2. Find the magnitude of v: 6
3. Substitute the values into the expression 2w - (1/3)v: 2(9/2) - (1/3)(6)
4. Calculate: 18 - 2 = 16
5. Take the absolute value and round to the nearest tenth: 16.0 (rounded to the nearest tenth)

Therefore, the magnitude of 2w - (1/3)v is approximately 16.0 (rounded to the nearest tenth).

Learn more about Magnitude of Vectors