(1) a⃗⋅b⃗=1⋅2+5⋅4+3⋅7=2+20+21=43\vec{a} \cdot \vec{b} = 1 \cdot 2 + 5 \cdot 4 + 3 \cdot 7 = 2 + 20 + 21 = 43a⋅b=1⋅2+5⋅4+3⋅7=2+20+21=43 a⃗×b⃗=∣ijk153247∣=(35−12)i+(6−7)j+(4−10)k=23i−j−6k∴(23,−1,−6)\vec{a} \times \vec{b} = \begin{vmatrix} i & j & k \\ 1 & 5 & 3 \\ 2 & 4 & 7 \end{vmatrix} = (35-12)i + (6-7)j + (4-10)k = 23i - j - 6k \qquad \therefore (23,-1,-6)a×b=i12j54k37=(35−12)i+(6−7)j+(4−10)k=23i−j−6k∴(23,−1,−6) (2) a⃗⋅b⃗=5⋅3+7⋅(−1)+(−2)⋅2=4\vec{a} \cdot \vec{b} = 5 \cdot 3 + 7 \cdot (-1) + (-2) \cdot 2 = 4a⋅b=5⋅3+7⋅(−1)+(−2)⋅2=4 a⃗×b⃗=∣ijk57−23−12∣=(14−2)i+(−6−10)j+(−5−21)k=12i−16j−26k∴(12,−16,−26)\vec{a} \times \vec{b} = \begin{vmatrix} i & j & k \\ 5 & 7 & -2 \\ 3 & -1 & 2 \end{vmatrix} = (14-2)i + (-6-10)j + (-5-21)k = 12i - 16j - 26k \qquad \therefore (12,-16,-26)a×b=i53j7−1k−22=(14−2)i+(−6−10)j+(−5−21)k=12i−16j−26k∴(12,−16,−26)