 Good morning friends. I am Poojwa and today we will discuss the following question show that the vectors 2 i cap minus j cap plus k cap i cap minus 3 j cap minus 5 k cap and 3 i cap minus 4 j cap minus 4 k cap from the vertices of a right-angled triangle Let us begin with the solution now now let Vector a b is equal to 2 i cap minus j cap plus k cap Vector bc is equal to i cap minus 3 j cap minus 5 k cap and Vector ca is equal to 3 i cap minus 4 j cap minus 4 k cap Now we have to show that these three vectors from the vertices of a right-angled triangle So for that we will show that the sum of square of magnitudes of any of the two vectors is equal to The square of magnitude of the third vector. So first we will find the Magnitude of vector a b vector bc and vector ca now model vector a b is equal to under root of 2 square plus minus 1 square plus 1 square and This is equal to under root of 4 plus 1 plus 1 which is equal to under root 6 So model vector a b is equal to root 6 model vector bc is equal to under root of 1 square plus minus 3 square plus minus 5 square and This is equal to under root of 1 plus 9 plus 25 Which is equal to under root 35? So model vector bc is equal to under root 35 and Finally, model vector ca is equal to under root of 3 square plus minus 4 square plus minus 4 square and This is equal to under root of 9 plus 16 plus 16 Which is equal to under root 41 So model vector ca is equal to under root 41 now we can clearly see that model vector a b square plus model vector bc square is equal to 6 plus 35 which is equal to 41 and This is equal to model vector ca square Therefore, we have shown that model vector a b square plus model vector bc square is Equal to model vector ca square That is we have shown that sum of squares of magnitudes of vector a b and vector bc is Equal to square of magnitude of vector ca hence we have The given vectors form the vertices of a right angle triangle This is our answer. Hope you have understood the solution. Bye and take care