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Question

The area of the triangle formed by the two vectors A = 3^i + 4^j and B = 3^i + 7^j is.

A
33 sq. unit
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B
21 sq. unit
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C
0 sq. unit
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D
332 sq. unit
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Solution

The correct option is D 332 sq. 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 = 33.

So area of triangle = 12|A × B| = 332sq.unit


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