MHT CET · Maths · Vector Algebra
If \(\bar{c}=5 \bar{a}+6 \bar{b}\) and \(3 \bar{c}=\bar{a}-4 \bar{b}\) then
- A \(\bar{a}, \bar{b}, \bar{c}\) are non-collinear
- B \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) are in the same direction
- C \(\overline{\mathrm{a}}, \overline{\mathrm{c}}\) are in the same direction but \(\overline{\mathrm{a}}, \overline{\mathrm{b}}\) are in the opposite direction
- D \(\bar{c}, \bar{b}\) are in the opposite direction and \(\bar{a}, \bar{b}\) are in the same direction
Answer & Solution
Correct Answer
(C) \(\overline{\mathrm{a}}, \overline{\mathrm{c}}\) are in the same direction but \(\overline{\mathrm{a}}, \overline{\mathrm{b}}\) are in the opposite direction
Step-by-step Solution
Detailed explanation
\(3(5\bar{a} + 6\bar{b}) = \bar{a} - 4\bar{b}\) \(15\bar{a} + 18\bar{b} = \bar{a} - 4\bar{b}\)
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