Find the magnitude of the vector v = (3, -4, 12).

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Question: Find the magnitude of the vector v = (3, -4, 12).

Options:

Correct Answer: 14

Solution:

Magnitude |v| = √(3^2 + (-4)^2 + 12^2) = √(9 + 16 + 144) = √169 = 13.

Find the magnitude of the vector v = (3, -4, 12).

Find the magnitude of the vector v = (3, -4, 12).

Correct Answer: 13

Step 1: Identify the components of the vector v. The vector v = (3, -4, 12) has three components: 3, -4, and 12.
Step 2: Square each component of the vector. Calculate 3^2, (-4)^2, and 12^2.
Step 3: Calculate 3^2 = 9.
Step 4: Calculate (-4)^2 = 16.
Step 5: Calculate 12^2 = 144.
Step 6: Add the squared values together. Add 9 + 16 + 144.
Step 7: Calculate the sum. 9 + 16 = 25, and then 25 + 144 = 169.
Step 8: Take the square root of the sum. Calculate √169.
Step 9: Find the square root. √169 = 13.
Step 10: The magnitude of the vector v is 13.

Vector Magnitude – The magnitude of a vector in three-dimensional space is calculated using the formula |v| = √(x^2 + y^2 + z^2), where x, y, and z are the components of the vector.