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AP EAMCET Engineering 26 Apr 2017 Shift 1 Paper

Section: Mathematics

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Question : 29 of 160

Marks: +1, -0

\left(\overset{-}{3i}-\overset{-}{j}+\overset{-}{2k}\right)=\left(\overset{-}{2i}+\overset{-}{3j}-\overset{-}{k}\right)x+\left(\overset{-}{i}-\overset{-}{2j}+\overset{-}{2k}\right)y+\left(-\overset{-}{2i}+\overset{-}{j}-\overset{-}{2k}\right)z,

is

(2,-5,3)
(2,5,-3)
(-2,5,3)
(2,5,3)

Solution:

It is given that,

\left(\overset{-}{3i}-\overset{-}{j}+\overset{-}{2k}\right)=(\left(\overset{-}{2i}+\overset{-}{3j}-\overset{-}{k}\right)x

+\left(\overset{-}{i}-\overset{-}{2j}+\overset{-}{2k}\right)y+\left(-\overset{-}{2i}+\overset{-}{j}-\overset{-}{2k}\right)z)

= [ \overline{i}(2 x+y-2 x)+\overline{j}(3 x-2 y+z)

+\overline{k}(-x+2 y-2 z) ]

Compare the coefficient of like terms.

2 x+y-2 z=3

3 x-2 y+z=-1

-x+2 y-2 z=2

On solving the three equations,

x=2

y=5

z=3

Therefore,

(x, y, z)=(2,5,3)

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