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Question

If A = 6i -8j and B = - 16i + 5j , what is the magnitude of the vector C = 2A - B ?

Answer 1

First, we find C in terms of i and j:

 

C = 2A - B

C = 2(6j - 8j) - (-16i + 5j)

C = 12i - 16j +16i - 5j

C = 28i - 21j

 

Now we can use the Pythagorean theorem, aka, the length formula, to find the length of C:

 

|C| = sqrt(28² + (-21)²)

|C| = sqrt(784 + 441)

|C| = sqrt(1225)

|C| = 35

 

A shortcut on that last calculation would be to notice that 28 = 7*4, and 21 = 7*3, so the two coordinates are in the ratio 4:3. That means we're looking at something similar to a 3:4:5 right triangle, and the magnitude must be 7*5, or 35.