Find a + b, a − b, 4a + 5b, 4a − 5b, and ||a ||.

Question

Find a + b, a − b, 4a + 5b, 4a − 5b, and ||a||

a = −6,-4)

b=3(0,4)

,

a+b=

a-b=

4a+5b=

4a-5b=

||a||=

Answer 1

To make solving the problems easier, first start by distributing the factors outside of the vectors:

a = (-6,4) b = (0, 12)

When adding and subtracting vectors, add/subtract the corresponding components of the vectors:

a + b = (-6+0, 4+12) = (-6, 16)

a - b = (-6-0, 4-12) = (-6, -8)

4a + 5b = 4(-6,4) + 5(0,12) = (-24,16) + (0,60) = (-24, 76)

4a - 5b = 4(-6,4) - 5(0,12) = (-24,16) - (0,60) = (-24, -44)

To find the magnitude of a, square each component of the vector, add, and take the square root:

||a|| = √((-6)²+(4)²) = √(36+16) = √52 = 2√13

Hope this helps!