diketahu vektor p = i+2j-k dan q = 4i+j+2k Tentukan vektor r yang memenuhi persamaan berikut = a) vektor r = 2p+3q . , b) 3p=r+4q ., c)p+2q-3r =0 ..d) 3p-2r+4q=

p = i + 2j - k
q = 4i + j + 2k

a.
r = 2p + 3q
r = 2(i + 2j - k) + 3(4i + j + 2k)
r = 2i + 4j - 2k + 12i + 3j + 6k
r = 14i + 7j + 4k

b.
3p = r + 4q
3(i + 2j - k) = r + 4(4i + j + 2k)
3i + 6j - 3k = r + 16i + 4j + 8k
3i + 6j - 3k - 16i - 4j - 8k = r
-13i + 2j - 11k = r

c.
p + 2q - 3r = 0
i + 2j - k + 2(4i + j + 2k) - 3r = 0
i + 2j - k + 8i + 2j + 4k - 3r = 0
9i + 4j + 3k - 3r = 0
-3r = -9i - 4j - 3k
r = 3i + 4/3j + k

d.
3p - 2r + 4q = p + 2q
3(i + 2j - k) - 2r + 4(4i + j + 2k) = i + 2j - k + 2(4i + j + 2k)
3i + 6j - 3k - 2r + 16i + 4j + 8k = i + 2j - k + 8i + 2j + 4k
19i + 10j + 5k - 2r = 9i + 4j + 3k
-2r = 9i + 4j + 3k - 19i - 10j - 5k
-2r = -10i - 6j - 2k
r = 5i + 3j + k