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Multiplication with Vectors

Find the area...

Question

Find the area of the parallelogram whose sides are represented by $2^i + 4^j - 6^k$ and $^i + 2^k .$

A

6.7

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B

13.4

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C

26.8

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D

53.6

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Solution

The correct option is D 13.4
Area of the parallelogram is the magnitude of cross product of vectors representing sides.
$A = ∣ ∣ ∣ (2 \land i + 4 \land j - 6 \land k) X (1 \land i + 2 \land k) ∣ ∣ ∣$
$= ∣ ∣ ∣ ∣ \begin{matrix} i & j & k 2 & 4 & - 6 1 & 0 & 2 \end{matrix} ∣ ∣ ∣ ∣ = | 8 i - 10 j - 4 k | = 13.4$

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