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Q.

The statement whether given is true or false?

If , where x, y, z are not all zero, then

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a

True

b

False

answer is B.

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Detailed Solution

The given statement is false.
Concept- First, we will need to substitute any of the variables, say z, i.e., the value of z given in the question statement in the other two equations, and express the other two variables, x and y in terms of their ratios. Then we will have to equate the ratios x:y for the two equations and find the relations between the coefficients a, b, c. Finally, using the relations between the coefficients a, b, c, we will find out whether the given final statement in the question is true or false.
The three given equations in the question are as follows:
Question Image

Question Image

Thus substituting

from the equation (iii) in the equation (i) and (ii) respectively, we get,

Simplifying equation (iv), we get,
Question Image

Question Image

Similarly, simplifying equation (v), we get,
Question Image

Question Image

Since,

,

Question Image

Hence, the given statement is false.

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