For the following three vectors, what is ·(2 Upper A Overscript right-arrow EndS
ID: 1528111 • Letter: F
Question
For the following three vectors, what is ·(2 Upper A Overscript right-arrow EndScripts times Upper B Overscript right-arrow EndScripts)? Upper A Overscript right-arrow EndScripts equals 3.00 i Overscript EndScripts plus 3.00 j Overscript EndScripts minus 3.00 k Overscript EndScripts Upper B Overscript right-arrow EndScripts equals negative 3.00 i Overscript EndScripts plus 3.00 j Overscript EndScripts plus 3.00 k Overscript EndScripts Upper C Overscript right-arrow EndScripts equals 7.00 i Overscript EndScripts minus 9.00 j Overscript EndScripts
Explanation / Answer
A = 3i + 3j - 3k
B = -3i + 3j + 3k
c = 7i - 9j
R = 3 C . (2A X B)
2A x B = (6i + 6j - 6k ) X (-3i + 3j + 3k)
= 18k - 18j + 18k + 18i + 18j + 18i
= 36i + 36k
R = (21i - 27j) . (26i + 36k)
= (21 x 26) + (-27 x 0) + (0 x 36)
= 546