Find the distance between points P(1,−3,4)P(1, -3, 4)P(1,−3,4) and Q(−4,1,2)Q(-4, 1, 2)Q(−4,1,2).
Using the formula: d=(x2−x1)2+(y2−y1)2+(z2−z1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}d=(x2−x1)2+(y2−y1)2+(z2−z1)2 d=(−4−1)2+(1−(−3))2+(2−4)2d = \sqrt{(-4 - 1)^2 + (1 - (-3))^2 + (2 - 4)^2}d=(−4−1)2+(1−(−3))2+(2−4)2 d=(−5)2+(4)2+(−2)2d = \sqrt{(-5)^2 + (4)^2 + (-2)^2}d=(−5)2+(4)2+(−2)2 d=25+16+4=45d = \sqrt{25 + 16 + 4} = \sqrt{45}d=25+16+4=45 d=35 unitsd = 3\sqrt{5} \text{ units}d=35 units
Show that the points A(−2,3,5)A(-2, 3, 5)A(−2,3,5), B(1,2,3)B(1, 2, 3)B(1,2,3) and C(7,0,−1)C(7, 0, -1)C(7,0,−1) are collinear.
Point Coordinates
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