If the direct cosines of two lines are such that l+m+n=0, l 2 +m 2 -n 2 =0, then the angle between them is ?

Question

Vikas TU · Answer

Dear Student, l+m+n=0 => l+m=−n => −(l+m) = n -------- (1) and l2+m2−n2=0 ----- (2) Substitute for n in equation (2) we get l2+m2−l2−m2−2ml=0 or 2ml=0 => l=0 or m=0. Put m=0 in equation (1). If m=0, then l=−n and direction ratios are (l,m,n)=(1,0,−1). Let us put l=0, we get m=−n, direction ratios are (l,m,n)=(0,1,−1). (l 1 , m 1 , n 1 ).(l 2 , m 2 , n 2 ) = (1,0,−1).(0,1,−1) = 0+0+1 = 1 Now substituting the above values in cosθ = b1.b2/|b1||b2| cosθ = 1/√2√2 = 1/2 => θ= π/3. Cheers!! Regards, Vikas (B. Tech. 4 th year Thapar University)

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

If the direct cosines of two lines are such that l+m+n=0, l 2 +m 2 -n 2 =0, then the angle between them is ?

If the direct cosines of two lines are such that l+m+n=0, l²+m²-n²=0, then the angle between them is ?

1 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Analytical Geometry

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

If the direct cosines of two lines are such that l+m+n=0, l 2 +m 2 -n 2 =0, then the angle between them is ?

If the direct cosines of two lines are such that l+m+n=0, l2+m2-n2=0, then the angle between them is ?

1 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Analytical Geometry

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

If the direct cosines of two lines are such that l+m+n=0, l²+m²-n²=0, then the angle between them is ?