1) You have three vectors with (∣v⃗∣,θ)(∣v∣,θ) pairs of (11,75∘)(11,75∘), (8,50∘)(8,50∘), and (10,−100∘)(10,−100∘). If you wanted...

1) You have three vectors with (∣v⃗∣,θ)(∣v∣,θ) pairs of (11,75∘)(11,75∘), (8,50∘)(8,50∘), and (10,−100∘)(10,−100∘).

If you wanted to add a fourth vector to those first three such that the sum of all four vectors were 0, what would that fourth vector be? Give your answer as a (vx,vy)(vx,vy) pair. Give your answer to 1 decimal point. Then show it as a (∣v⃗∣,θ)(∣v∣,θ) pair.

Solutions

Expert Solution

Let the given vectors be

Their components in the x direction are

Their components in the y direction are

Let Vx and Vy be the x-component and y-component of the required vector V, respectively.

Given, sum of all four vectors should be zero.

therefore, sum of their components in the x direction is zero

therefore, sum of their components in the y direction is zero

Magnitude of the vector V is

Angle vector V makes with the negative x-axis

therefore, angle of vector V is

Therefore, the fourth vector is

genius_generous answered 1 year ago

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