Using vectors ,find the value k such that points (k,-10,3),(1,-1,3) and (3,5,3) are collinear - Maths - Vector Algebra

Question

Using vectors ,find the value k such that points
(k,-10,3),(1,-1,3) and (3,5,3) are collinear

Anuradha Sharma · Accepted Answer

We know the points A,B,C are collinear if area of triangle ABC=0Now p
v  of A=ki^-10j^+3k^p v  of B=i^-j^+3k^p v
 of C=3i^+5j^+3k^AB→ =p v
 of B- p v
 of A=i^-j^+3k^-ki^-10j^+3k^=1-ki^+9j^AC→ =p v
 of C- p v
 of A=3i^+5j^+3k^-ki^-10j^+3k^=3-ki^+15j^Now area will be zero so, AB→  ×AC→=i^j^k^1-k903-k150=0i^ 0-j^0+k^15-15k-27+9k=0i^+0j^+0k^comparing we get,-6k-12=0k=-2

Using vectors ,find the value k such that points (k,-10,3),(1,-1,3) and (3,5,3) are collinear.