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Question

Calculate the area of the triangle determined by the two vectors A=3^i+4^j and B=3^i+7^j


A

0sq unit

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B

20sq unit

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C

16.5sq unit

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D

12.4sq unit

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Solution

The correct option is C

16.5sq unit


We know that the half of magnitude of the cross product of two vectors gives the area of the triangle.
A×B=∣ ∣ ∣^i^j^k340370∣ ∣ ∣=^i(00)^j(00)+^k(21+12)=33^k
Taking magnitude |A×B|=332
So area of triangle =12|A×B|=332=16.5sq unit


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