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Question

The two adjacent sides OA,OB of parallelogram are 2^i+4^j5^k and ^i+2^j+3^k. The unit vectors along the diagonals of the parallelogram are given by

A
(3^i+6^j2^k)7
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B
(^i2^j+8^k)69
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C
(3^i6^j+2^k)7
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D
(^i+2^j8^k)69
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Solution

The correct option is A (3^i+6^j2^k)7

Given that,

OA=2^i+4^j5^k

OB=^i+2^j+3^k


Now, one diagonal of a parallelogram

P=A+B

P=(2^i+4^j5^k)+(^i+2^j+3^k)

P=3^i+6^j2^k


Now, unit vector along the diagonal

^P=P|P|

^P=3^i+6^j2^k9+36+4

^P=3^i+6^j2^k7


Hence, the unit vectors along the diagonals of the parallelogram is 3^i+6^j2^k7


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