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Area of rectangle having vertices A, B, C and D will position vector (-i^+12j^+4k^),(i^+12j^+4k^)(i^-12j^+4k^) and (-i^-12j^+4k^) is -

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Question

Area of rectangle having vertices A, B, C and D will position vector `(- hati + 1/2hatj + 4hatk), (hati + 1/2hatj + 4hatk) (hati - 1/2hatj + 4hatk)` and `(-hati - 1/2hatj + 4hatk)` is

Options

  • `1/2` sq.units

  • 1 sq.units

  • 2 sq.units

  • 4 sq.units

MCQ

Solution

2 sq.units

Explanation:

The position vectors of A and B are `- hati + 1/2 hatj + 4hatk` and `hati + 1/2 hatj + 4hatk`

∴ `vec(AB) = [1 - (-1)hati + 0 * hatj + 0 * hatk]`

∴ `|vec(AB)|` = 2

The position vectors of A and D are `-hati + 1/2hatj + 4hatk` and `-hati - 1/2hatj + 4hatk`

∴ `vec(AD) = (-hati + hati) + (- 1/2 - 1/2)hatj + (4hatk - 4hatk) = - hati`

`|vec(AD)|` = 1

∴ Area of rectangle ABCD = `|vec(AB)||vec(AD)| = 2 xx 1` = 2

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