COMEDK · Maths · 33. Vector Algebra
\(\text { If } \hat{\imath}+\hat{\jmath}-\hat{k} \quad \&~ 2 \hat{\imath}-3 \hat{\jmath}+\hat{k} \text { are adjacent sides of a parallelogram, then length of its diagonals are }\)
- A \(\sqrt{3}, \quad \sqrt{14}\)
- B \(\sqrt{21}, \quad \sqrt{13}\)
- C \(\sqrt{13}, \sqrt{14}\)
- D \(\sqrt{21}, \quad \sqrt{3}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{21}, \quad \sqrt{13}\)
Step-by-step Solution
Detailed explanation
Let the adjacent sides of the parallelogram be represented by vectors \(\vec{a} = \hat{i} + \hat{j} - \hat{k}\) and \(\vec{b} = 2\hat{i} - 3\hat{j} + \hat{k}\). The diagonals of the parallelogram are given by \(\vec{d_1} = \vec{a} + \vec{b}\) and…
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