Question

The direction cosines of a line satisfy the relation l(l + m)

= n, mn + nl + lm = 0.

The value of l, for which the two lines are perpendicular to each other is-

• A. 1
• B. 2
• C. 1/2
• D. None of these

Answer 1

Answer: (B)

2

Answer 2

For l = –m +, the second relation gives

mn + n $\left( - \mathrm { m } + \frac { \mathrm { n } } { \lambda } \right) + \mathrm { m } \left( - \mathrm { m } + \frac { \mathrm { n } } { \lambda } \right)$= 0

or n2 + mn – lm2 = 0 ̃$\frac { \mathrm { n } ^ { 2 } } { \mathrm {~m} ^ { 2 } } + \frac { \mathrm { n } } { \mathrm { m } }$– l = 0.

If $\frac { \mathrm { n } _ { 1 } } { \mathrm {~m} _ { 1 } }$, $\frac { \mathrm { n } _ { 2 } } { \mathrm {~m} _ { 2 } }$are its roots then $\frac { \mathrm { n } _ { 1 } \mathrm { n } _ { 2 } } { \mathrm {~m} _ { 1 } \mathrm {~m} _ { 2 } }$= – l

̃

Since the lines are perpendicular –1 –1 + l = 0