What is the converse of the following true conditional? if the converse is true, rewrite the statements as a biconditional. if either is false, give a counterexample. if two lines are parallel, they do not intersect. select one: a. if two lines do not intersect, they are parallel. one statement is false. if two lines do not intersect, they could be skew. b. if two lines do not intersect, they are parallel. one statement is false. if two lines are parallel, they may intersect twice. c. if two lines do not intersect, they are parallel. both statements are true. two lines are parallel if (and only if) they do not intersect. d. if two lines do not intersect, they are not parallel. both statements are true. two lines are not parallel if (and only if) they do not intersect.

A

Step-by-step explanation: The converse of a conditional is when the two statements switch spots, for example:

Conditional: If someone like ice cream, they have brown hair

Converse: If someone has brown hair, they like ice cream

The converse of our given conditional would be:

If two lines do not intersect, they are parallel

This eliminates Option D

Next, the converse is false.

Skew lines (example attached) do not intersect and are also not parallel, meaning if two lines do not intersect, they could be either parallel or skew.

This eliminates Option C and B, leaving us with Option A

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step-by-step explanation:

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the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12