Show that the line segment joining the origin to the point A(2, 1, 1)

1.	Show that the line segment joining the origin to the point A(2, 1, 1) is perpendicular to the line segment joining the points B(3, 5, -1) and C(4,3, -1).
Answer» Given: O(0, 0, 0) and A(2, 1, 1) The line joining these two points is given by, OA = 2i + j +k B(3, 5, -1) and D(4, 3, -1), The line joining these two points, BC = i - 2j +0k To prove that the two lines are perpendicular we need to show that the angle between these two lines is So, OA.BC = 0 (dot product) Thus, (2i + j +k). (i - 2j +0k) = 2 - 2 + 0 = 0. Thus, the two lines are perpendicular

Show that the line segment joining the origin to the point A(2, 1, 1) is perpendicular to the line segment joining the points B(3, 5, -1) and C(4,3, -1).

Answer»

Given: O(0, 0, 0) and A(2, 1, 1)

The line joining these two points is given by,

OA = 2i + j +k

B(3, 5, -1) and D(4, 3, -1),

The line joining these two points,

BC = i - 2j +0k

To prove that the two lines are perpendicular we need to show that the angle between these two lines is

So, OA.BC = 0 (dot product)

Thus, (2i + j +k). (i - 2j +0k) = 2 - 2 + 0 = 0.

Thus, the two lines are perpendicular

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Show that the line segment joining the origin to the point A(2, 1, 1) is perpendicular to the line segment joining the points B(3, 5, -1) and C(4,3, -1).

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