Question

Given A = i - 2j +3k and B = 3i - 2j + k find 2A + 5B.

Answer 1

We have A = \(\hat i\) - 2\(\hat j\) + 3\(\hat k\)

and 3 = 3\(\hat i\) - 2\(\hat j\) + \(\hat k\)

2A + 5B = 2(\(\hat i\) -  2\(\hat j\) + 3\(\hat k\)) + 5 (3\(\hat i\) - 2\(\hat j\) + \(\hat k\))

= (2\(\hat i\) - 4\(\hat j\) + 6\(\hat k\) ) + (15\(\hat i\) - 10\(\hat j\) + 5\(\hat k\))

= (2 + 15)\(\hat i\) - (4 + 10)\(\hat j\) + (6 + 5)\(\hat k\)

= 17 \(\hat i\) - 14 \(\hat j\) + 11\(\hat k\)