Find the sum of the vectors a = i + 6j + k and c = i - 6j - 5k.

Add the vectors a = i + 6j + k, b = 6i + 4j + 5k and c = i - 6j - 5k by writing them in the component form that is a = <1, 6, 1>, b = <6, 4, 5> and c = <1, -6, -5>. Then the sum of the vectors can be computed as follows:
a + b + c = <1 + 6 + 1, 6 + 4 - 6, 1 + 5 - 5> = <8, 4, 1>
Hence the sum of the vectors is <8, 4, 1> = 8i + 4j + k.