​ Show that the points whose position vectors are vector(5i+ 6j+ 7k, 7i− 8j+ 9k and 3+ 20j+ 5k) are collinear. ​

Question

Show that the points whose position vectors are 5\(\hat i\)+ 6\(\hat j\)+ 7\(\hat k\), 7\(\hat i\)− 8\(\hat j\)+ 9\(\hat k\) and 3\(\hat i\)+ 20\(\hat j\)+ 5\(\hat k\) are collinear.

Answer 1

Given that the position vector of points , and are 5\(\hat i\)+ 6\(\hat j\)+ 7\(\hat k\), 7\(\hat i\)− 8\(\hat j\)+ 9\(\hat k\) and 3\(\hat i\)+ 20\(\hat j\)+ 5\(\hat k\), respectively.

Hence, the points , and are collinear. 

Hence, the points whose position vectors are ( 5\(\hat i\)+ 6\(\hat j\)+ 7\(\hat k\), ), ( 7\(\hat i\)− 8\(\hat j\)+ 9\(\hat k\) ) and 3\(\hat i\)+ 20\(\hat j\)+ 5\(\hat k\)  are collinear.