Vector Magnitudes and Simplifying Square Roots

This video tutorial explains how to calculate the magnitude of the difference between two vectors, c and d, and how to subtract the magnitudes of these vectors. It covers the step-by-step process of finding vector differences, calculating magnitudes, and simplifying results using prime factorization. The tutorial also highlights the importance of identifying perfect square factors for simplification.

What is the first step in finding the magnitude of vector C minus vector D?

• Add the x and y components of vectors C and D.

• Subtract the x and y components of vectors C and D.

• Multiply the x and y components of vectors C and D.

• Divide the x and y components of vectors C and D.

What is the x component of the vector resulting from C minus D?

• -10

• 6

• 10

• -6

How do you simplify the square root of 136?

• By finding the cube root of 136.

• By dividing 136 by 2.

• By adding 136 to itself.

• By finding the prime factorization of 136.

What is the simplified form of the square root of 136?

• 5 times the square root of 34

• 3 times the square root of 34

• 2 times the square root of 34

• 4 times the square root of 34

What is the magnitude of vector C?

• Square root of 60

• Square root of 40

• Square root of 100

• Square root of 80

What is the magnitude of vector D?

• Square root of 100

• Square root of 40

• Square root of 80

• Square root of 60

How can the square root of 80 be simplified?

• As the square root of 2 times 40

• As the square root of 16 times 5

• As the square root of 4 times 20

• As the square root of 8 times 10

What is the simplified form of the square root of 80?

• 4 times the square root of 5

• 5 times the square root of 5

• 3 times the square root of 5

• 2 times the square root of 5

What is the simplified form of the square root of 40?

• 5 times the square root of 10

• 3 times the square root of 10

• 4 times the square root of 10

• 2 times the square root of 10

What is the final result of the magnitude subtraction?

• 5 square root 5 minus 3 square root 10

• 2 square root 5 minus 4 square root 10

• 4 square root 5 minus 2 square root 10

• 3 square root 5 minus 5 square root 10