AP EAMCET · Maths · Vector Algebra
Let \(\mathbf{u}, \mathbf{v}\) and \(\mathbf{w}\) be three vectors in \(R^3\). Then, any vector \(Z \in \mathbf{R}^3\) can be written as \(z=a \mathbf{u}+b \mathbf{v}+c \mathbf{w}\) for some scalars \(a, b\) and \(c\) if and only if
- A Each pair of \(\mathbf{u}, \mathbf{v}\) and \(\mathbf{w}\) are not parallel
- B Each of \(\mathbf{u}, \mathbf{v}\) and \(\mathbf{w}\) can be written as a linear combination of the other two
- C All have different magnitude and directions
- D None of the options are correct
Answer & Solution
Correct Answer
(D) None of the options are correct
Step-by-step Solution
Detailed explanation
As given vector \(u, v\) and \(\mathbf{w}\) given may be not parallel but they may be antiparallel So, \(\mathbf{z} \neq a \mathbf{u}+b \mathbf{v}+c \mathbf{w}\) So first is incorrect. Also, if \(\mathbf{u}=\mathbf{v}+\mathbf{w}\)…
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