

InterviewSolution
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A line makes an angle of 30° and 60° with the positive direction of X and Y-axis. Find the angle formed by the line with the positive direction of Z-axis.1. 60°2. 30°3. 45°4. 90°5. 140° |
Answer» Correct Answer - Option 4 : 90° Concept: The direction cosines of a vector are the cosines of the angles between the vector and the three +ve coordinate axes i.e. X, Y, Z axes. l2 + m2 + n2 = 1 where l = the cosines of the angles between the vector and X-axis. m = the cosines of the angles between the vector and Y-axis. n = the cosines of the angles between the vector and Z-axis. Calculation: Let the line makes an angle γ with the positive direction of Z-axis. Thus it makes angle 30°, 60° and γ with the three axes. ∴ the d.c's of line are cos 30°, cos 60°, cos γ i. e. \(\dfrac{\sqrt{3}}{2}\), \(\dfrac{1}{2}\), cos γ we know that, l2 + m2 + n2 = 1 ∴ \({\left( {\sqrt 3 /2} \right)^2} + {\left( {1/2} \right)^2} + {\left( {\cos γ } \right)^2} = 1\) or cos2 γ = 1 - 1 ⇒ cos2 γ = 0 ⇒ cos γ = 0 or, γ = 90° Thus the line makes an angle of 90° with the Z-axis. |
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