Question

If $\mathbf { a } , \mathbf { b } , \mathbf { c }$ be any three non-zero non-coplanar vectors, then any vector $\mathbf { r }$ is equal to

• A. $z \mathbf { a } + x \mathbf { b } + y \mathbf { c }$
• B. $x \mathbf { a } + y \mathbf { b } + z \mathbf { c }$
• C. $y \mathbf { a } + z \mathbf { b } + x \mathbf { c }$
• D. None of these

Answer 1

Answer: (B)

$x \mathbf { a } + y \mathbf { b } + z \mathbf { c }$

Answer 2

Where , , As $\mathbf { a } , \mathbf { b } , \mathbf { c }$ are three non-coplanar vectors, we may assume

$\mathbf { r } = \alpha \mathbf { a } + \beta \mathbf { b } + \gamma \mathbf { c }$

=

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But ; $\therefore \alpha = x$

Similarly $\beta = y , \gamma = z$ ; $\therefore$ $\mathbf { r } = x \mathbf { a } + y \mathbf { b } + z \mathbf { c }$