 Good morning friends, I am Purva and today I will help you with the following question. Show that the vectors 2i cap minus 3j cap plus 4k cap and minus 4i cap plus 6j cap minus 8k cap are collinear. Suppose vector a and vector b are two vectors such that vector a is equal to lambda times vector b where lambda is some scalar. Then we say either vector a is parallel to vector b or vector a and vector b are collinear. So this is the key idea behind our question. Let us now begin with the solution. Let position vector of pb 2i cap minus 3j cap plus 4k cap and position vector of qb minus 4i cap plus 6j cap minus 8k cap. Let o be the origin then we have vector op is equal to position vector of p minus position vector of o and which is equal to 2i cap minus 3j cap plus 4k cap and vector oq is equal to position vector of q minus position vector of o and it is equal to minus 4i cap plus 6j cap minus 8k cap. Now taking out minus 2 common from where we get vector oq is equal to minus 2 into 2i cap minus 3j cap plus 4k cap. This is equal to minus 2 into now 2i cap minus 3j cap plus 4k cap is equal to vector op. So we get vector oq is equal to minus 2 into vector op. Now from key idea we know that if a vector is equal to some scalar times another vector then either the two vectors are parallel to each other or they are collinear. So we have either vector oq is parallel to vector op or vector oq and vector op are collinear because here we have minus 2 as the scalar. So we get either vector oq is parallel to vector op or vector oq and vector op are collinear. But o is the common point so these two vectors can't be parallel therefore we have the given vectors are collinear. This is our answer. Hope you have understood the solution. Bye and take care.