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TS EAMCET · Maths · Vector Algebra

If \(\mathbf{a}=2 \mathbf{u}+3 \mathbf{v}+7 \mathbf{w}, b=\mathbf{u}+\mathbf{v}-2 \mathbf{w}\) and \(\mathbf{c}=-\mathbf{u}-2 \mathbf{v}-3 \mathbf{w}\) then \(\left|\frac{\left[\begin{array}{ll}\mathbf{u} & \mathbf{v}\end{array}\right]}{\left[\begin{array}{lll}\mathbf{a} & \mathbf{b} & \mathbf{c}\end{array}\right]}\right|(\mathbf{a}+\mathbf{b}+\mathbf{c})=\)

  1. A \(12(u+v+w)\)
  2. B \(3(u+v+w)\)
  3. C \(\frac{2}{3}(u+v+w)\)
  4. D \(\frac{1}{3}(u+v+w)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1}{3}(u+v+w)\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { Given, } \mathbf{a}=2 \mathbf{u}+3 \mathbf{v}+7 \mathbf{w} \\ & \mathbf{b}=\mathbf{u}+\mathbf{v}-2 \mathbf{w} \\ & \mathbf{c}=-\mathbf{u}-2 \mathbf{v}-3 \mathbf{w} \\ & \mathbf{a}+\mathbf{b}+\mathbf{c}=2(\mathbf{u}+\mathbf{v}+\mathbf{w}) \\ &…