Q11 of 112 Page 1134

Show that the lines x = - y = 2z and x + 2 = 2y – 1 = - z + 1 are perpendicular to each other.

HINT: The given lines are and


Given –


&


To prove – The lines are perpendicular to each other


Direction ratios of L1 = (2,-2,1)


Direction ratios of L2 = (2,1,-2)


Tip – If (a,b,c) be the direction ratios of the first line and (a’,b’,c’) be that of the second, then the angle between these pair of lines is given by


The angle between the lines






Hence, the lines are perpendicular to each other.


More from this chapter

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9

Show that the lines and are perpendicular to each other.

 10

If the lines and are perpendicular to each other then find the value of λ.

 12

Find the angle between two lines whose direction ratios are

i. 2, 1, 2 and 4, 8, 1


ii. 5, -12, 13 and -3, 4, 5


iii. 1, 1, 2 and


iv. a, b, c and (b – c), (c – a), (a – b)


 13

If A(1, 2, 3), B(4, 5, 7), C(-4, 3, -6) and D(2, 9, 2) are four given points then find the angle between the lines AB and CD.