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Question

If a=^i+^j+^k and b=2^i+0^j+^k then the vectors c satisfying the conditions, (i) that it is coplanar with a and b (ii) that it is perpendicular to b, and (iii) that a.c=7, is

A
32^i+52^j+3^k
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B
3^i+5^j+6^k
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C
6^i+0^j+5^k
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D
^i+2^j+2^k
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Solution

The correct option is A 32^i+52^j+3^k
Given
a=^i+^j+^k
b=2^i+0^j+^k
Let c = x^i+y^j+z^k
If a,b,c are coplanar [a,b,c]=0
111201xyz
x+3y-2z=0 - (1)
c is prependicular to b
c.b=0
2x+z=0
a.c=7 - (2)
-x+y+z=7 - (3)
Solving (1), (2) and (3) we get
c=12(3^i+5^j+6^k)

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