Calculations with vectors

a = 3i +4j, b = -7i + 24j, c = i – 2j, d = 3j

a) Find |a|
b) Find |b|

|a| = sqrt(3^2+4^2)

about 5 I think. Now you do the other. Remember when you square a negative you get a positive.

To find the magnitude (or length) of a vector, you can use the formula:

|v| = √(x^2 + y^2 + z^2)

where x, y, and z are the components of the vector. In this case, we are given vectors a, b, c, and d in terms of their components, so we can use this formula to find their magnitudes.

a) To find |a|, we can substitute the given components into the formula:

|a| = √((3)^2 + (4)^2)

Simplifying this expression gives:

|a| = √(9 + 16)
|a| = √25
|a| = 5

Therefore, the magnitude of vector a, denoted as |a|, is 5.

b) To find |b|, we can substitute the given components into the formula:

|b| = √((-7)^2 + (24)^2)

Simplifying this expression gives:

|b| = √(49 + 576)
|b| = √625
|b| = 25

Therefore, the magnitude of vector b, denoted as |b|, is 25.