00:01
We are provided with position vectors, oa, equals to 2 icap plus j cap minus 2k cap and ob equals to 2 icp minus j cap plus 2k cap, oc equals to icap plus 3j cap plus 3kkkkk and in first part we are asked to find the vector equation of line b c.
00:37
As we know, vector equation of line is given by r equals to a plus lambda times b vector.
00:55
Here a vector is 2 i -caf minus j -capped plus 2 k -caf and b vector is given by oc vector.
01:05
Minus ob vector, which is equals to ikep plus 4 j cap plus k -cab.
01:15
So the vector equation of line b -c is given by 2 i -kep minus j -cap plus 2 k -cap plus lambda times minus i -kep plus 4 j -caf plus k -cab plus k -kap.
01:39
So this is the final answer for part a.
01:49
In part b, we have to check whether or not the lines oa and b c intersect.
01:57
So oa is 2 ic plus j cap minus 2 k cap and bc is given by oc minus b which is equals to minus icp plus minus icp plus.
02:19
4 j cap plus k cap clearly all the three components of oa and b c are not equal at the point of intersection so from here we can conclude that oa and b c do not intersect so this is the final answer for part b in part c we have to find out the cartesian equation of the plane e which passes through c and is perpendicular to oe...