Question

show that the three points a(1 -2 3) b(2 3 -4) and c(0 -7 10) are collinear​

Answer 1

Answer:

Hence Proven

Step-by-step explanation:

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Answer 2

The three points a(1, -2, 3), b(2, 3, -4), and c(0, -7, 10) are not collinear.

To show that three points are collinear, we need to show that they lie on the same straight line.

We can use the vector equation of a straight line in 3D to determine if the three points are collinear or not. The vector equation of a straight line passing through point A (x1, y1, z1) and directed along vector v = (a, b, c) is given by:

r = A + t v, where t is a parameter.

If three points are collinear, they will lie on the same straight line, which means that we can find a vector v that is parallel to the line passing through the three points.

To find a vector that is parallel to the line passing through a and b, we can subtract the position vectors of these points:

v1 = b - a = (2 - 1, 3 - (-2), -4 - 3) = (1, 5, -7)

Similarly, to find a vector that is parallel to the line passing through b and c, we can subtract the position vectors of these points:

v2 = c - b = (0 - 2, -7 - 3, 10 - (-4)) = (-2, -10, 14)

If the three points are collinear, then the vector v1 must be parallel to the vector v2. We can check if this is true by calculating the cross product of v1 and v2. If the cross product is zero, then the vectors are parallel.

v1 x v2 = (1, 5, -7) x (-2, -10, 14)

= (70, 0, 0)

Since the cross product is a non-zero vector, we can conclude that the vectors v1 and v2 are not parallel, and therefore the points a, b, and c are not collinear.

for such more question on collinear​

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