COMEDK · Maths · 33. Vector Algebra
If the vectors \(\mathrm{a}=2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}} ; \mathrm{b}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}}\) and \(\mathrm{c}=m \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}\) are coplanar, then the value of \(m\) is
- A \(\dfrac{2}{3}\)
- B \(\dfrac{8}{5}\)
- C \(\dfrac{-7}{4}\)
- D \(\dfrac{5}{8}\)
Answer & Solution
Correct Answer
(B) \(\dfrac{8}{5}\)
Step-by-step Solution
Detailed explanation
Three vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) are coplanar if and only if their scalar triple product is zero, which is given by the determinant of the matrix formed by their components. The condition is \(\vec{a} \cdot (\vec{b} \times \vec{c}) = 0\), which implies:…
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