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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

  1. A None of \(\mathbf{u}\) and \(\mathbf{v}\) is a scalar multiple of the other
  2. B None of \(|u|\) and \(|v|\) is a scalar multiple of the other
  3. C \(u\) and \(v\) have different direction
  4. D \(u\) and \(v\) are perpendicular to each other
Verified Solution

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…