What is the angle made by the vector - i - 5j with x-axis?
Correct answer: D. 270 - tan-1(1/5)
- A. tan-1(1/5)
- B. 90 + tan-1(1/5)
- C. 180 + tan-1(1/5)
- D. 270 - tan-1(1/5)
Explanation
If both components of a vector are negative, then the vector resides in the third quadrant of Cartesian Coordinate System. For which we have the formula θ= 180o +|yx| .But the answers are given in the form of xy .Using the properties of the inverse trigonometric functionsxy+xy=2 -----(3)And xy=1xy =yx By substituting this into equation 3 we getxy+yx=90o Or yx=90o-xy Now we can have our answer in the form of xy θ=180o+90o-xy θ=270o-tan-1xyHence, we have the angle: θ=270o-15
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