To calculate the cross product of (-u - 3w) and w, we can use the properties of the cross product.

The cross product is distributive over addition and scalar multiplication, so we can write:

(-u - 3w) × w = -u × w - 3w × w

We know that u × w = ⟨−4,−4,1⟩, so -u × w = -⟨−4,−4,1⟩ = ⟨4,4,-1⟩.

The cross product of any vector with itself is the zero vector, so w × w = ⟨0,0,0⟩.

Therefore, (-u - 3w) × w = ⟨4,4,-1⟩ - 3⟨0,0,0⟩ = ⟨4,4,-1⟩.

Question

To calculate the cross product of (-u - 3w) and w, we can use the properties of the cross product.

The cross product is distributive over addition and scalar multiplication, so we can write:

(-u - 3w) × w = -u × w - 3w × w

We know that u × w = ⟨−4,−4,1⟩, so -u × w = -⟨−4,−4,1⟩ = ⟨4,4,-1⟩.

The cross product of any vector with itself is the zero vector, so w × w = ⟨0,0,0⟩.

Therefore, (-u - 3w) × w = ⟨4,4,-1⟩ - 3⟨0,0,0⟩ = ⟨4,4,-1⟩.

Knowee AI · Accepted Answer

To calculate the cross product of (-u - 3w) and w, we can use the properties of the cross product.

The cross product is distributive over addition and scalar multiplication, so we can write:

(-u - 3w) × w = -u × w - 3w × w

We know that u × w = ⟨−4,−4,1⟩, so -u × w = -⟨−4,−4,1⟩ = ⟨4,4,-1⟩.

The cross product of any vector with itself is the zero vector, so w × w = ⟨0,0,0⟩.

Therefore, (-u - 3w) × w = ⟨4,4,-1⟩ - 3⟨0,0,0⟩ = ⟨4,4,-1⟩.

Calculate the cross product assuming that u×w=⟨−4,−4,1⟩ (−u−3w)×w=