COMEDK · Maths · 34. Three Dimensional Geometry
The direction cosines of the vector \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\) is equal to
- A \(\frac{2}{3}, \frac{1}{3},-\frac{2}{3}\)
- B \(\frac{2}{3}, \frac{1}{3}, \frac{2}{3}\)
- C \(\frac{1}{3}, \frac{2}{3},-\frac{2}{3}\)
- D \(\frac{2}{3}, \frac{2}{3}, \frac{1}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{2}{3}, \frac{1}{3},-\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
Let \(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\) So, \(\quad|\mathfrak{a}|=\sqrt{4+1+4}=\sqrt{9}=3\) So, direction cosines of vector are \(\frac{2}{3}, \frac{1}{3},-\frac{2}{3}\).
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