Question

Two vectors represented as A=3i+4j and B=2i_4k find the unit vector parallel to

Answer 1

Explanation:

Solution:

The given vectors are

a = 3i - j - 4k = (3,-1,-4),

b=

= -2i+ 4j - 3k = (- 2, 4, -3) and

c = i + 2j-k= (1, 2, -1)

Then p = (3a - 2b + 4c)

= 3 (3,-1,- 4) - 2 (- 2, 4, - 3) + 4 (1, 2, - 1)

= (9, -3, -12) + (4, - 8, 6) + (4, 8, -4)

= (9 + 4 + 4,-3-8+8, -12 + 6-4)

= (17, -3, -10)

= 17i - 3j - 10k

Now the unit vector parallel to p is the unit vector along its direction; determined by

p/p, where p=lpl

= (17i - 3j - 10k) / | 17i - 3j - 10k |

= (17i - 3j - 10k)/√(17² +3² +10²)

= (17i - 3j - 10k) / √398