Question 10 (Or 1st) - CBSE Class 12 Sample Paper for 2019 Boards
Last updated at Oct. 30, 2019 by Teachoo

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Question 10 (OR 1
st
question)

Find the area of the parallelogram whose diagonals are represented by the vectors a = 2i – 3j + 4k and b = 2i – j + 2k

We use the
Area of Parallelogram formula with Diagonals

Transcript

Question 10 (OR 1st question) Find the area of the parallelogram whose diagonals are represented by the vectors ๐ โ = 2๐ ฬ โ 3๐ ฬ + 4๐ ฬ and ๐ โ = 2๐ ฬ โ ๐ ฬ + 2๐ ฬ
Area of parallelogram with diagonals
Area = 1/2 |(๐_1 ) โร(๐_2 ) โ |
Given Diagonals of a parallelogram as
๐ โ = 2๐ ฬ โ 3๐ ฬ + 4๐ ฬ
and ๐ โ = 2๐ ฬ โ ๐ ฬ + 2๐ ฬ
Area of the parallelogram = 1/2 |๐ โร๐ โ |
Finding ๐ โ ร ๐ โ
๐ โ ร ๐ โ = |โ 8(๐ ฬ&๐ ฬ&๐ ฬ@2&โ3&4@2&โ1&2)|
= ๐ ฬ ((โ3) ร 2 โ (-1) ร 4) โ ๐ ฬ (2 ร 2 โ 2 ร 4) + ๐ ฬ (2 ร (-1) โ 2 ร (-3))
= ๐ ฬ (-6 + 4) โ ๐ ฬ (4 โ 8) + ๐ ฬ (โ2 + 6)
= ๐ ฬ (โ2) - ๐ ฬ (โ4) + ๐ ฬ (4)
= โ2๐ ฬ + 4๐ ฬ + 4๐ ฬ
So,
Magnitude of ๐ โ ร ๐ โ = โ((โ2)2+(4)2+(4)2)
|๐ โ" ร " ๐ โ | = โ(4+16+16)
|๐ โ" ร " ๐ โ |= โ36
|๐ โ" ร " ๐ โ |= 6
Thus,
Area of the parallelogram = 1/2 |๐ โร๐ โ |
= 1/2 ร 6
= 3 square units

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