Maths · Straight line: Various forms of equations of a line, intersection of lines, angles between two lines
If the points with position vectors and are collinear then
If the points with position vectors \( 60 \hat{i}+ \) \( \mathbf{3} \hat{\mathbf{j}}, \mathbf{4 0} \hat{\mathbf{i}}-\mathbf{8} \hat{\mathbf{j}} \) and \( \boldsymbol{a} \hat{\mathbf{i}}-\mathbf{5 2} j \) are collinear then \( a=? \)
- A. -40
- B. -20
- C. 20
- D. 40
Step-by-step solution
Points are collinear if the slope between any two pairs is equal. Slope AB = (-8 - 3) / (40 - 60) = (-11) / (-20) = 11/20. Slope BC = (-52 - (-8)) / (a - 40) = (-44) / (a - 40). Set equal: -44/(a-40) = 11/20 => -880 = 11a - 440 => 11a = -440 => a = -40.
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