Show that the points whose position vectors are -2i+3j, i+2j+3k and 7i-k are collinear
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Suppose A, B and C are the points which are represented by;
A⃗ = −2i+3j ; B⃗ = i+2j+3k and C⃗ = 7i−k
Coordinates of these points are A(-2, 3, 0); B(1, 2, 3) and C(7, 0, -1).
So, AB −→−= (1+2,2−3,3−0) = (3,−1,3)AC −→− = (7+2,0−3,−1−0) = (9,−3,−1)
∣3 −1 3|
|9 -3 -1|
= 3(1+9)+1(−327)+3(−9+9) = 0
Therefore, points A, B and C are collinear.
A⃗ = −2i+3j ; B⃗ = i+2j+3k and C⃗ = 7i−k
Coordinates of these points are A(-2, 3, 0); B(1, 2, 3) and C(7, 0, -1).
So, AB −→−= (1+2,2−3,3−0) = (3,−1,3)AC −→− = (7+2,0−3,−1−0) = (9,−3,−1)
∣3 −1 3|
|9 -3 -1|
= 3(1+9)+1(−327)+3(−9+9) = 0
Therefore, points A, B and C are collinear.
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