AP EAMCET · Maths · Vector Algebra
The set of all real values of c so that the angle between the vectors \(\overline{\mathrm{a}}=\mathrm{cx} \overline{\mathrm{i}}-6 \overline{\mathrm{j}}+3 \overline{\mathrm{k}}\) and \(\overline{\mathrm{b}}=x \overline{\mathrm{i}}+2 \overline{\mathrm{j}}+2 \mathrm{cx} \overline{\mathrm{k}}\) is an obtuse angle for all real \(x\) is
- A \(\left(0, \frac{4}{3}\right]\)
- B \(\left(0, \frac{2}{3}\right]\)
- C \(\left(-\frac{2}{3}, 0\right)\)
- D \(\left(\frac{-4}{3}, 0\right]\)
Answer & Solution
Correct Answer
(D) \(\left(\frac{-4}{3}, 0\right]\)
Step-by-step Solution
Detailed explanation
\(\overline{\mathrm{a}} \cdot \overline{\mathrm{b}} \((\mathrm{cx})(x) + (-6)(2) + (3)(2\mathrm{cx}) \(\mathrm{cx}^2 + 6\mathrm{cx} - 12 If \(c=0\): \(-12 If \(c \neq 0\): For \(Ax^2+Bx+C\(c \((6c)^2 - 4(c)(-12) \(36c^2 + 48c \(12c(3c + 4) For \(12c(3c+4) Combining…
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