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

Question

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

a = i + 3j,     b = 8i − 2j

a + b	=
a − b	=
4a + 5b	=
4a − 5b	=
||a||	=

Answer 1

Hi Abhi P.,

With a = i + 3j and b = 8i - 2j:

a + b = (1+8)i + (3-2)j = 9i + j

a - b = (1-8)i + (3+2)j = -7i + 5j

4a + 5b = (4i + 12j) + (40i - 10j) = (4+40)i + (12-10)j = 44i +2j

4a - 5b = (4i + 12j) - (40i - 10j) = (4-40)i + (12+10)j = -36i + 22j

||a|| = √(1² + 3²) = √(10)

I hope this helps, Joe.