AP EAMCET · Maths · Three Dimensional Geometry
Let \(\mathbf{u}\) and \(\mathbf{v}\) be two vectors in a plane. Then any vector \(\mathbf{w}\) in the plane can be written as \(w=a \mathbf{u}+b \mathbf{v}\) for some scalars ' \(a\) ' and ' \(b\) ' if and only if
- A None of \(\mathbf{u}\) and \(\mathbf{v}\) is a scalar multiple of the other
- B None of \(|u|\) and \(|v|\) is a scalar multiple of the other
- C \(u\) and \(v\) have different direction
- D \(u\) and \(v\) are perpendicular to each other
Answer & Solution
Correct Answer
(B) None of \(|u|\) and \(|v|\) is a scalar multiple of the other
Step-by-step Solution
Detailed explanation
Any vector \(\mathbf{w}\) in the plane containing vector \(\mathbf{u}\) and \(\mathbf{v}\) can be written as \(\mathbf{w}=a \mathbf{u}+b \mathbf{v}\) for some scalars ' \(a\) ' and ' \(b\) ' if and only if \(\mathbf{u}\) and \(\mathbf{v}\) vectors are not parallel means none of…
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