Question 1: Calculate the magnitude |v| of the vector v with components x=3 and y=4.

Answer: 5

Question 2: Find the magnitude |v| of a vector with components x=−6 and y=8.

Answer: 10

Question 3: Determine |v| for the vector with x=0 and y=7.

Answer: 7

Question 4: Calculate |v| for the vector with x=−5 and y=−12.

Answer: 13

Question 5: If a vector v has |v|=10 and x=6, find the value of y.

Answer: 8

Question 6: A vector has components x=−8 and y=15. Confirm its magnitude and explain your calculation.

Answer: 15.0; |v|=√(−8)² + 15²=√64+225=√289=17

Question 7: Construct a triangle on the grid with sides representing vectors of magnitude 5 and 12, with the third side of magnitude 13. Verify the side lengths using |v|=√(x² + y²).

Answer: Yes; sides 5, 12, 13 satisfy the Pythagorean theorem: 5²+12²=13²

Question 8: A vector v has components x and y such that |v|=20. If x=12, find y, showing all steps.

Answer: y=16

Question 9: A vector with components x=−9 and y=−40 is drawn. Calculate its magnitude and comment on the sign of components.

Answer: |v|=√(−9)² + (−40)²=√81+1600=√1681=41; signs indicate direction quadrant

Question 10: A vector v has components x = 7, y = 24. Calculate |v| and interpret its significance.

Answer: 25

Question 11: Identify the common mistake in calculating |v| for a vector with components x=−3 and y=4, where a student incorrectly computes |v| as 7. Correct the mistake.

Answer: Incorrect; |v|=√(−3)² + 4²=√9+16=√25=5. The student added x and y, which is wrong.