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Question
Find →A×→B, if →A=^i+2^j−4^k and →B=2^i−^j+2^k.
Find →A×→B, if →A=^i+2^j−4^k and →B=2^i−^j+2^k.
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Solution
The correct option is C −10^j−5^k
It is given that, →A=^i+2^j−4^k and →B=2^i−^j+2^k.
For finding the cross-product, we use determinant method. The respective coefficients for ^i,^j,^k are placed in the determinant format, shown below:
→A×→B=∣∣
∣
∣∣^i^j^k12−42−12∣∣
∣
∣∣=^i((2)(2)−(−1)(−4))−^j((2)−(−8))+^k((−1)−(4))=−10^j−5^k
Hence option C is the correct answer.
It is given that, →A=^i+2^j−4^k and →B=2^i−^j+2^k.
For finding the cross-product, we use determinant method. The respective coefficients for ^i,^j,^k are placed in the determinant format, shown below:
→A×→B=∣∣ ∣ ∣∣^i^j^k12−42−12∣∣ ∣ ∣∣=^i((2)(2)−(−1)(−4))−^j((2)−(−8))+^k((−1)−(4))=−10^j−5^k
Hence option C is the correct answer.
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