Given →p=3^i+2^j+4^k,→a=^i+^j,→b=^j+^k,→c=^i+^k and →P=x→a+y→b+z→c, then x,y,z are respectively.
A
32,12,52
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B
12,32,52
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C
52,32,12
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D
12,52,32
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Solution
The correct option is B12,32,52 →p=x→a+y→b+z→c ⇒3^i+2^j+4^k=x(^i+^j)+y(^j+^k)+z(^i+^k) ⇒3^i+2^j+4^k=(x+z)^i+(x+y)^j+(y+z)^k On comparing both sides the coefficients of ^i,^j,^k, we get x+z=3 ...........(i) x+y=2 ...........(ii) and y+z=4 ...........(iii) On solving Eqs. (i),(ii) and (iii), we get X=12,y=32,z=52