3 years ago

The prime factorization of 56

Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

6 0

The prime factores are 7,2,2,2

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Determine if the lines r1(t) = <3, 0, 2> + t <1, 2, −2> and r2(s) = <0, 1, −1> + s <4, 1, 1> intersect,

Temka [501]

Answer:

Yes lines are intersecting, point of intersection is <4,2,0>.

Step-by-step explanation:

Given parametric equations of line are:

$r_{1}(t) = + t \\ r_{1}(t) = \\ r_{1}(t) = ---(1)$

$r_{2}(s) = + s \\ r_{2}(s) = \\ r_{2}(s) = ---(2)\\$

If lines are intersecting then parametric coordinates of (1) are equal to (2)

$3+t=4s---(A)\\2t=1+s---(B)\\2-2t=s-1---(C)\\$

Considering A and B to find values of t and s

From A

t=4s-3---(D)

Putting in (B)

2(4s-3)=1+s

8s-6=1+s

7s=7

s=1

Then

t=4-3

t=1

If lines are intersecting then these values of s and t must satisfy (C)

2-2(1)=1-1

0=0

This shows lines are intersecting.

At this value of t, (1) becomes

$r_{1}(1) = \\=$

Putting s=1 in (2)

$r_{2}(1)=4, 1+1,-1+1>\\=$

Point of intersection is <4,2,0>.

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3 years ago