(adsbygoogle = window.adsbygoogle || []).push({}); 1.Consider the two straight lines:

2λi+(1+4λ)j+(3-3λ)k

(4+μ)i+(3+5μ)j+(-6+μ)k

a) Show lines are skew when a=3.

b) Find value of a for which lines intersect and state coordinates of point of intersection

2.

2λi+(1+4λ)j+(3-3λ)k=(4+μ)i+(3+5μ)j+(-6+μ)k

comparing i components:

(1)

2λ=4+μ

λ=(4+μ)/2

comparing j components:

(2)

1+4λ=3+5μ

λ=(2+5μ)/4

(1)=(2)

(4+μ)/2=(2+5μ)/4

16+4μ=4+10μ

μ=2

sub into (1)

λ=(4+μ)/2

λ=(4+2)/2

λ=3

Different values so the lines are skew

d) Find a value of a for which the lines intersect and state the coordinates of the point of intersection.

r1=2λi+(4λ+1)j+(a-3λ)k

r2=(μ+4)i+(5μ+3)j+(μ-6)k

I need to find the value of a for which the lines intersect and state the coordinates of point of intersection.

λ=3

μ=2

LHS a-3λ=μ-6

a-3(3)=2-6

a-9=-4

a=5

r2=4i+3j-6k+μ[i+5j+k]

r2=4i+3j-6k+2[i+5j+k]

r2=4i+3j-6k+2i+10j+2k

6i+13j-4k

coordinates of point of intersection are:

(6, 13, -4)

could somebody tell me if i'm on the right track here please?

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# Homework Help: Intersecting vector lines

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