Diketahui p=4i+2j-k, q=-6i+j-2k, r=i+5j+4k Ditanya:1.

1. -2i+3j-3k, 2. 7i+4j+6k, 3. -20, 4. -13i+17j-18k, 5. -29

Pembahasan

Diketahui vektor p=4i+2j-k, q=-6i+j-2k, r=i+5j+4k.
1. p+q = (4-6)i + (2+1)j + (-1-2)k = -2i + 3j - 3k
2. r-q = (1-(-6))i + (5-1)j + (4-(-2))k = 7i + 4j + 6k
3. q.p (hasil kali skalar q dan p) = (-6)(4) + (1)(2) + (-2)(-1) = -24 + 2 + 2 = -20
4. rxp (hasil kali vektor r dan p) = | i  j  k |
                           | 1  5  4 |
                           | 4  2 -1 |
         = i((-5)-(8)) - j((-1)-(16)) + k((2)-(20))
         = -13i + 17j - 18k
5. q.(p+r) = q.p + q.r
   q.p = -20 (dari no 3)
   q.r = (-6)(1) + (1)(5) + (-2)(4) = -6 + 5 - 8 = -9
   q.(p+r) = -20 + (-9) = -29