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Question

The sides of a parallelogram are 2^i+4^j5^k and ^i+2^j+3^k. The unit vector parallel to one of the diagonals is

A
17(3^i+6^j2^k)
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B
17(3^i6^j2^k)
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C
169(^i+2^j+8^k)
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D
169(^i2^j+8^k)
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Solution

The correct option is A 17(3^i+6^j2^k)
Adjacent sides of a parallelogram are given as:
a=2ˆi+4ˆj5ˆkandb=ˆi+2ˆj+3ˆk
Then, the diagonal of a parallelogram is given by
a+ba+b=(2+1)^i+(4+2)^j+(5+3)^k=3^i+6^j2^ka+b|a|+b=3^i+6^j2^k9+36+4=3^i+6^j2^k7=37^i+67^j27^k=17(3^i+6^j2^k)

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