v=⟨4,9,4⟩v=⟨4,9,4⟩ w=⟨7,10,6⟩w=⟨7,10,6⟩Find the cosine of the angle between vv and ww.

To find the cosine of the angle between two vectors, we use the formula:

cos(θ) = (v . w) / (||v|| ||w||)

where:

• v . w is the dot product of v and w
• ||v|| is the magnitude of v
• ||w|| is the magnitude of w

Step 1: Find the dot product of v and w v . w = (47) + (910) + (4*6) = 28 + 90 + 24 = 142

Step 2: Find the magnitude of v ||v|| = sqrt((4^2) + (9^2) + (4^2)) = sqrt(16 + 81 + 16) = sqrt(113)

Step 3: Find the magnitude of w ||w|| = sqrt((7^2) + (10^2) + (6^2)) = sqrt(49 + 100 + 36) = sqrt(185)

Step 4: Substitute these values into the formula cos(θ) = 142 / (sqrt(113) * sqrt(185)) = 142 / (sqrt(20905)) = 0.98

So, the cosine of the angle between v and w is approximately 0.98.