Find the vector, not with determine, but by using properties of croos products. a) k×(i−7j) b) (i+j)×(i−j) If a=⟨2, −1, 2⟩ and b=⟨5, 2, 1⟩, find the following a×b=? b×a=?

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Find the vector, not with determine, but by using properties of croos products. a) k×(i−7j) b) (i+j)×(i−j) If a=⟨2, −1, 2⟩ and b=⟨5, 2, 1⟩, find the following a×b=? b×a=?

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Step 1 We recall the cross product property that i×i=0 j×j=0 k×k=0 i×j=k j×k=i k×i=j  j×i=−k k×j=−i i×k=−j Step 2 Answer 1: We need to find k×(i−7j) k×(i−7j)=k×i−7(k×j) =−j−7(−i) =7i−1j+0k Step 3 Answer 2: Now we find: (i+j)×(i−j) (i+j)×(i−j)=i×(i−j)+j×(i−j) (i+j)×(i−j)=i×i−i×j+j×i−j×j (i+j)×(i−j)=0−k+(−k)−0 (i+j)×(i−j)=−2k Step 4 Answer 3: Given: a=⟨2, −1, 2⟩ and b=⟨5, 2, 1⟩ a×b=⟨2, −1, 2⟩×⟨5, 2, 1⟩ Using distributive property and the properties of cross product a×b=4k−2j+5k−1i+10j−4i a×b=−5i+8j+9k Now we find b×a b×a=⟨5, 2, 1⟩×⟨2, −1, 2⟩ b×a=−5k−10j−4k+4i+2j+1i b×a=5i−8j−9k

Find the vector, not with determine, but by using properties of croos products.

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