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Question

Side and diagonal of a parallellogram are given by vectors a=3^i+2^j^k and d1=2^i+4^j+2^k.

A
Another side of parallelogram may be ^i+2^j+3^k
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B
Another diagonal may be 4^i4^j4^k
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C
Area of parallelogram is 83 unit
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D
Area of parallelogram is 8^i+64^j
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Solution

The correct options are
A Another side of parallelogram may be ^i+2^j+3^k
C Area of parallelogram is 83 unit
Another side is b.
Depending on whether d1 is the larger or the smaller diagonal, there are two possibilities.
a+b=d1 or ab=d1
b=d1a or b=(d1a)
b=^i+2^j+3^k or b=^i2^j3^k
ab=d2d2=4^i4^k
Area=a×b=∣ ∣ ∣^i^j^k321123∣ ∣ ∣=8^i8^j+8^k
|Area|=82+82+82=83

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