Vector Components and Magnitudes

The video tutorial explains how to find the value of 'a' in a vector v, where the x component is 'a' and the y component is 'b', given that b equals 40 and the magnitude of vector v is 41. The process involves using the magnitude formula, substituting known values, and solving the resulting equation. The solution is found by squaring both sides of the equation, isolating 'a', and taking the square root, considering only the positive value as specified. The final result is that 'a' equals 9, making the vector v in component form (9, 40).

What is the y-component of vector v?

• 30

• 40

• 50

• 60

What is the magnitude of vector v?

• 42

• 41

• 40

• 39

Which formula is used to calculate the magnitude of a vector?

• a^2 - b^2

• sqrt(a^2 + b^2)

• a^2 + b^2

• a + b

What is the value of 41 squared?

• 1600

• 1700

• 1681

• 1640

What operation is performed to both sides of the equation to remove the square root?

• Addition

• Subtraction

• Multiplication

• Squaring

After simplifying, what is the value of a squared?

• 83

• 82

• 80

• 81

What is the square root of 81?

• 10

• 9

• 7

• 8

Why is only the positive value of 'a' considered?

• a is always positive

• a is given as positive

• a cannot be negative

• a is a component

What is the final value of the x-component of vector v?

• 9

• 8

• 10

• 7

What are the final components of vector v?

• (8, 41)

• (9, 41)

• (8, 40)

• (9, 40)