Question

Find the angle between two straight lines whose direction cosines are l1 m1 n1 and l2 m2 n2

Answer 1

Step-by-step explanation:

Given Find the angle between two straight lines whose direction cosines are l1 m1 n1 and l2 m2 n2

• Let a1 = (l1, m1,n1) be a unit vector along one line
•   So a2 = (l2,m2,n2) be a unit vector along other line.
• So a1 x a2 be unit vector perpendicular to both a1 and a2
•            So a1 x a2 =  i          j        k
•                                  l 1       m1    n1
•                                 l 2        m2    n2
•       using the formula we get      
• cos theta = a1a2 + b1b2 + c1c2 / √a1^2 + b1^2 + c1^2√a2^2 + b2^2 + c2^2
•        so a1 x a2 = i(m1n2 – n1m2) – j(n1 l2 – l1n2) + k (l 1 m2 – m1l2)
•        so cosines will be m1n2 – n1m2, n1l2 – l1n2, l1m2 – m1l2
• Therefore the angle is given by  
• cos theta = mod a1a2 + b1b2 + c1c2 / √a1^2 + b1^2 + c1^2 √a2^2 + b2^2 + c2^2

Reference link will be

https://brainly.in/question/10558975