# Which pair of the lines are parallel? Given the following:a) 2x+2y+2=0, `vecr`=(1,2) +s(1,-1) b) x+7y-2=0, `vecr`=(2,5) +s(1,7) c) 3x-4y-2=0, `vecr`=(1,4) +s(-3,-1) d) none of the above.

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### 1 Answer

a) You need to find the direction vectors of the lines such that:

`bar v_1 = lt2,2gt ; bar v_2 = lt1,-1gt`

You need to remember that two vectors are parallel if the coressponding components of both vectors are in the same ratio.

`2/1 != 2/(-1)`

**Hence, the lines `2x+2y+2=0` and `bar r = (1,2) + s(1,-1)` are not parallel.**

b) You need to find the direction vectors of the lines such that:

`bar v_1 = lt1,7gt ; bar v_2 = lt1,7gt`

You need to check if coressponding components of both vectors are in the same ratio.

`1/7 = 1/7`

**Hence, the lines `x+7y-2=0 ` and `bar r = (2,5) + s(1,7)` are parallel.**

c) You need to find the direction vectors of the lines such that:

`bar v_1 = lt3,-4gt ; bar v_2 = lt-3,-1gt`

You need to check if coressponding components of both vectors are in the same ratio.

`3/(-3) != (-4)/(-1)`

**Hence, the lines `3x-4y-2=0` and `bar r = (1,4) + s(-3,-1) ` are not parallel.**