Write the angle between the lines whose direction ratios are proportional to 1, –2, 1 and 4, 3, 2.
Given,
• Direction Ratios of Line1 are proportional to (1,-2,1)
• Direction Ratios of Line2 are proportional to (4,3,2)
So we can say that,
Direction ratios of line1
a1 = 1 × k , b1 = (-2) × k and c1 = 1 × k
a1 = k , b1 = -2k and c1 = k
Direction ratios of line2
a2 = 4 × p , b2 = 3 × p and c2 = 2 × p
a2 = 4p , b2 = 3p and c2 = 2p
Now, the angle between the lines with direction ratios a1, b1, c1 and a2, b2, c2 is given by
By using this formula,
cos θ = 0
θ = 90°
The angle between the lines is 90°.