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lemon
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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?
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?