Question

let a=2i+j-3k,b=i-2j+k then the point of intersection of the lines

Answer 1

GIVEN :

Let a=2i+j-3k,b=i-2j+k

TO FIND :

The point of intersection of the lines

SOLUTION :

Given that a=2i+j-3k,b=i-2j+k

Then r x a = b x a

(r-b) x a = 0

r-b is ║ to "a"

∴ $r - b =\lambda a$

⇒ $r = b + \lambda a$

Similarly, we have that r x b = a x b can be written as

(r-a)x b=0

r-a is ║ to "b"

∴ $r - a =\mu b$

⇒ $r = a + \mu b$

The point of intersection of these two lines  is

$b + \lambda a = a + \mu b$

⇒ $\lambda = \mu = 1$

∴   the required point of intersection is

r = a+ b

= 2i+j-3k+i-2j+k

=3i-j-2k

 ∴   the required point of intersection is  r=3i-j-2k