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» It is given that Line joining O (0, 0, 0) and A (2, 1, 1) is written as OA = 2i + j + k Line joining B (3, 5, -1) and D (4, 3, -1) is written as BC = i – 2j + 0k In order prove that these two lines are perpendicular we must show that angle between these two lines is π/2 Dot product OA . BC = 0 Substituting the values (2i + j + k). (i – 2j + 0k) = 2 – 2 + 0 = 0 Hence, these 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»

It is given that

Line joining O (0, 0, 0) and A (2, 1, 1) is written as

OA = 2i + j + k

Line joining B (3, 5, -1) and D (4, 3, -1) is written as

BC = i – 2j + 0k

In order prove that these two lines are perpendicular we must show that angle between these two lines is π/2

Dot product OA . BC = 0

Substituting the values

(2i + j + k). (i – 2j + 0k) = 2 – 2 + 0 = 0

Hence, these two lines are perpendicular.