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TS EAMCET · Maths · Vector Algebra

If \(2 \hat{i}+3 \hat{j}-4 \hat{k}\) and \(-\hat{i}+2 \hat{j}+\hat{k}\) are the two diagonals of a parallelogram, then the area of the parallelogram in square units is

  1. A \(\frac{1}{2} \sqrt{170}\)
  2. B \(\sqrt{174}\)
  3. C \(\sqrt{\frac{87}{2}}\)
  4. D \(\frac{1}{4} \sqrt{174}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\sqrt{\frac{87}{2}}\)

Step-by-step Solution

Detailed explanation

Let \(\overrightarrow{\mathrm{d}}_1=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{d}}_2=-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\) Now Area is \(=\frac{1}{2} \overline{\mathrm{d}}_1 \times \overline{\mathrm{d}}_2\)…