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Question

If a=^i2^j+3^k,b=2^i+3^j^k and c=r^i+^j+(2r1)^k are three vectors such that c is parallel to the plane of a and b, then r is equal to?

A
0
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B
2
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C
1
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D
1
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Solution

The correct option is A 0
Given , ¯¯¯a=ˆi2ˆj+3ˆk¯¯b=2ˆi+3ˆj+ˆk¯¯c=rˆi+ˆj+(2r1)ˆk

also given that

¯¯cisparallelto¯¯¯aand¯¯bletusfindthevectortoboth¯¯¯aand¯¯b


¯¯¯aׯ¯b=∣ ∣ ∣ˆiˆjˆk123231∣ ∣ ∣

=ˆi(29)ˆj(16)+ˆk(3+4)¯¯¯aׯ¯b=7ˆi+7ˆj+7ˆk

rlinecisparallelto¯¯¯aand¯¯b
¯¯cwillparpendicularto¯¯¯aׯ¯b

¯¯c(¯¯¯aׯ¯b)=¯¯¯0
(rˆi+ˆj+(2r1)ˆk)(7ˆi+7ˆj+7ˆk)=¯¯¯0


r = 0






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