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Find the angle 0 (where 0º < 0 < 180°) between the given vectors. ū = 2i – 3j and ū = 3i +8j Round to the nearest hundredth of a degree (2 decimal places). Don't round your answer until the very end. 125.75 O 149.70 O None of these O 179.42 0 -30.30 359.42° O-.58 Find the angle 0 (where 0° << 180°) between the given vectors. ů = <2, – 5, 3> and ✓ = <5, 7, - 9> Round to the nearest degree (0 decimal places). Don't round your answer until the very end. Give your answer as a number without the degree symbol.



Answer :

To find the angle between two vectors, you can use the dot product formula:

θ = arccos((u ⋅ v) / (||u|| × ||v||))

where u and v are the two vectors, ||u|| and ||v|| are the magnitudes of the vectors u and v, and ⋅ is the dot product.

In the first problem, you are given that u = 2i - 3j and v = 3i + 8j. To find the angle between these vectors, you can first find the dot product of u and v:

u ⋅ v = (2i - 3j) ⋅ (3i + 8j)

= (23) + (-38)

= 6 - 24

= -18

Next, you can find the magnitudes of u and v:

||u|| = √((22) + (-3-3)) = √(13)

||v|| = √((33) + (88)) = √(73)

Now you can use the dot product formula to find the angle between the vectors:

θ = arccos((-18) / (√(13) × √(73)))

= arccos(-18 / 961)

You can use a calculator to find the value of arccos(-18 / 961), which is approximately 125.75 degrees.

In the second problem, you are given that u = <2, -5, 3> and v = <5, 7, -9>. To find the angle between these vectors, you can follow the same process as before:

u ⋅ v = (25) + (-57) + (3×-9) = 10 - 35 - 27 = -52

||u|| = √((22) + (-5-5) + (33)) = √(34)

||v|| = √((55) + (77) + (-9-9)) = √(109)

θ = arccos((-52) / (√(34) × √(109)))

= arccos(-52 / 3706)

You can use a calculator to find the value of arccos(-52 / 3706), which is approximately 179.42 degrees.

So the answer to the first problem is 125.75 degrees, and the answer to the second problem is 179.42 degrees.

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