Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

Find the angle between two lines whose directions cosines are given by l+m+n=0 and l^2+m^2-n^2=0.[**WITHOUT USING THEOREMS OF VECTOR**]

Asked by arjunsah797 | 02 May, 2022, 09:30: AM
Expert Answer
Given direction cosines are 
l+m+n = 0 ... (i)
l2 + m2 - n2 = 0 ... (ii)
From (i), we get, n = -(l+m)
Putting n in (ii)
l2 + m2 - (l+m)2 = 0
l2 + m2 - l2 - m2 - 2lm = 0
2lm = 0
Therefore, l = 0 or m = 0
Put l = 0 in (i), we get, n = -m
So, dorection ratios are (l, m, n) = (0, 1, -1)
Put m = 0 in (i), we get, n = -l
So, direction ratios are (l, m, n) = (1, 0, -1)
straight b with rightwards arrow on top subscript 1 times straight b with rightwards arrow on top subscript 2 equals open parentheses 0 comma space 1 comma space minus 1 close parentheses times left parenthesis 1 comma space 0 comma space minus 1 right parenthesis space equals space 0 plus 0 plus 1 space equals space 1
open vertical bar straight b with rightwards arrow on top subscript 1 close vertical bar equals square root of 2
open vertical bar straight b with rightwards arrow on top subscript 2 close vertical bar equals square root of 2
Now comma space cosθ equals fraction numerator straight b with rightwards arrow on top subscript 1 times straight b with rightwards arrow on top subscript 2 over denominator open vertical bar straight b with rightwards arrow on top subscript 1 close vertical bar open vertical bar straight b with rightwards arrow on top subscript 2 close vertical bar end fraction equals fraction numerator 1 over denominator square root of 2 square root of 2 end fraction equals 1 half
rightwards double arrow straight theta equals straight pi over 3
Answered by Renu Varma | 02 May, 2022, 11:16: AM
CBSE 12-science - Maths
Asked by arjunsah797 | 02 May, 2022, 09:30: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by lekhakarthikeyan | 09 Jan, 2019, 04:45: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 25 Feb, 2015, 08:55: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 25 Feb, 2015, 09:28: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 25 Feb, 2015, 11:00: AM
ANSWERED BY EXPERT

Start your hassle free Education Franchisee and grow your business!

Know more
×