Question

Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, –1) are collinear.

Answer 1

The given points are A( 1,2,7 ),B( 2,6,3 ) and C( 3,10,−1 ).

Let, ∠ABCbe given by θ,

AB → =( 2−1 ) i ^ +( 6−2 ) j ^ +(3−7) k ^ = i ^ +4 j ^ −4 k ^

| AB | → = 1 2 + 4 2 + 4 2 = 33

BC → =( 3−2 ) i ^ +( 10−6 ) j ^ +(−1−3) k ^ = i ^ +4 j ^ −4 k ^

| BC | → = 1 2 + 4 2 + (−4) 2 = 1+16+16 = 33

AC → =( 3−1 ) i ^ +( 10−2 ) j ^ +(−1−7) k ^ =2 i ^ +8 j ^ −8 k ^

| AC | → = 2 2 + 8 2 + 8 2 = 4+64+64 = 132 =2 33

Since | AC → |= | AB | → +| BC → |

Thus, the points A( 1,2,7 ),B( 2,6,3 ) ,and C( 3,10,−1 ) are collinear.