Example 7 - Find vector equation for line (-1, 0, 2), (3, 4, 6) - Equation of line  - given 2 points

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Example, 7 Find the vector equation for the line passing through the points ( 1, 0, 2) and (3, 4, 6). Vector equation Vector equation of a line passing though two points with position vectors and is = + ( ) Given, Let two points be A ( 1, 0, 2) & B(3, 4, 6) So, = ( + 0 + 2 ) + 3 +4 +6 ( + 0 + 2 ) = + 0 + 2 + 3 + 4 + 6 + 0 2 = + 0 + 2 + 3 + 1 + 4 0 + (6 2) = + 0 + 2 + 4 + 4 + 4 = + 2 + + + Therefore, the vector equation is + 2 + 4 + 4 + 4

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