TS EAMCET · Maths · Vector Algebra
If \(\alpha, \beta, \gamma\) are real numbers such that \(\left(\frac{7}{3}+\beta\right) \bar{i}-\bar{j}+(\alpha+\gamma) \bar{k}=\frac{5}{3}(\alpha \bar{i}+\bar{j}-\bar{k})+\beta(2 \bar{j}+\bar{k})+(\bar{i}+\gamma \bar{j}+3 \bar{k}), \text { then } 5 \alpha-9 \beta+13 \gamma=\)
- A 4
- B 12
- C 0
- D 15
Answer & Solution
Correct Answer
(B) 12
Step-by-step Solution
Detailed explanation
\begin{aligned} & \therefore\left(\frac{7}{3}+\beta\right) \hat{\mathrm{i}}-\hat{\mathrm{j}}+(\alpha+\gamma) \hat{\mathrm{k}}=\frac{5}{3}(\alpha \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}) \\ & +\mathrm{B}(2 \hat{\mathrm{j}}+\hat{\mathrm{k}})+(\hat{\mathrm{i}}+\mathrm{y}…
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