Q. 34.5( 35 Votes )

# Show that the lin

Answer :

We know that

Two lines with direction ratios a_{1}, b_{1}, c_{1} and a_{2}, b_{2}, c_{2} are parallel if the angle between them is θ = 0°, i. e.

⇒

Also, we know that the direction ratios of the line segment joining (x_{1}, y_{1}, z_{1}) and (x_{2}, y_{2}, z_{2}) is taken as x_{2} – x_{1}, y_{2} – y_{1}, z_{2} – z_{1} (or x_{1} – x_{2}, y_{1} – y_{2}, z_{1} – z_{2}).

⇒ The direction ratios of the line through the points (4, 7, 8) and (2, 3, 4) is:

a_{1} = 2 – 4 = -2, b_{1} = 3 – 7 = -4, c_{1} = 4 – 8 = -4

And the direction ratios of the line through the points (– 1, – 2, 1) and (1, 2, 5) is:

a_{2} = 1 – (-1) = 1 + 1 = 2, b_{2} = 2 – (-2) = 2 + 2 = 4, c_{2} = 5 – 1 = 4

Consider

⇒

∴ The line through the points (4, 7, 8), (2, 3, 4) is parallel to the line through the points (–1, –2, 1), (1, 2, 5).

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