Question

Question from 3D vector .

Find the point of intersection of line x-1 /2 = y-2/3 = z-3/4 and x-2/1 = y-4/2 = z+1/4 also find the angle between these two line .
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Answer 1

Solution

Step-by-step explanation:

given:- These two lines intersect,

let's, x-1/2= y-2/3= z-3/4 = L

x=2L+1, y = 3L +2 and z = 4L +3

similarly, in 2nd equation.

let's x-2/1 = y-4/2 = z+1/4 = m

x = m + 2 , y = 2m +4 , z = 4m -1

according two question, these line intersect .

since point will be same for that interaction .

so, 2L+1 = m + 2

2L -m = 1 ________(1) ×2

3L +2 = 2m +4

3L -2m = 2 _______(2).

From 1st and 2nd 2nd we get , L = 0 AND m = -1

So, point we have (2, 3,4 )

and , (1,2,-4)

cos¢ = p1q1+p2q2+p3q3 /√4+9+16√1+4+16

cos¢ = -8/√29√21 Answer .

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Hope it helps !!

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