Question

Show that the points a,b,c having position vectors ( i+2j+7k) , (2i+6j+3k) and (3i+10j-3k) respectively , are collinear .

Answer 1

Answer:

show, ab+bc = ac

Step-by-step explanation:

a------b-----c

a=i+2j+7k, b=2i+6j+3k, c=3i+10j-3k

then,

ab = (2i+6j+3k) - (i+2j+7k) = i+4j-4k

bc = (3i+10j-3k) - (2i+6j+3k) = i+4j-6k

ac = (3i+10j-3k) - (i+2j+7k) = 2i+8j-10k

Now,

ab+bc = (i+4j-4k)+(i+4j-6k) = 2i+8j-10k = ac

Hence, all the three given points are collinear.