COMEDK · Maths · 34. Three Dimensional Geometry
The vector \((\vec{r})\) whose magnitude is \(3 \sqrt{2}\) units which makes an angle of \(\dfrac{\pi}{4}\) and \(\dfrac{\pi}{2}\) with \(y\) and \(z\)- axis respectively is
- A \(-\hat{\imath} \pm \hat{\jmath}\)
- B \(\hat{\imath} \pm 3 \hat{\jmath}\)
- C \(\hat{\imath} \pm \hat{\jmath}\)
- D \(\pm 3 \hat{\imath}+3 \hat{\jmath}\)
Answer & Solution
Correct Answer
(D) \(\pm 3 \hat{\imath}+3 \hat{\jmath}\)
Step-by-step Solution
Detailed explanation
Direction cosines: \(m = \cos\dfrac{\pi}{4} = \dfrac{1}{\sqrt{2}}\), \(n = \cos\dfrac{\pi}{2} = 0\) Using \(l^2 + m^2 + n^2 = 1\): \(l^2 + \dfrac{1}{2} + 0 = 1 \Rightarrow l = \pm\dfrac{1}{\sqrt{2}}\)…
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