0:00
Hi everyone.
00:02
Hi everyone.
00:02
So in the given question, we are given that we have to find a unit vector which is orthogonal to these two vectors and whose have known negative first coordinate.
00:14
Okay.
00:14
So let's see that these two vectors.
00:18
The vector one which is equal to 6 icap plus 7 j cap plus 2 k cap.
00:26
Okay.
00:27
And the other vector which is equal to vector two.
00:31
Equal to 4 icap plus 7 times of j cap plus 7 k cap okay now the concept we are going to use here is called cross product cross product it means that vector 1 times vector 2 will give some another vector let's say v3 and this v3 vector is perpendicular to both v1 and b2 okay so using this we will just calculate so let's see.
01:08
Vector first is 6 icap plus 7 j cap plus 2 k cap cross of 4 i cap plus 7 j cap okay so we know that by i j and k rule we said that so which said that i cross j will result in k and k cross j i will result in j okay so this is the pattern for this okay now first i'm gonna multiply six with all the vectors okay so we know that six into four i do i cross i will be equal to zero and now multiplying it with it j cap so it will give 46 i close j cap okay plus six sevens are 42 i cross k cap similarly seven will be multiply with j cross i cap so it will be 28 actually okay because seven times four will be 28 plus we will get seven times seven j cap will be zero seven jkf times seven k cap will be like this okay and further we will multiply now this two so eight times k cap cross i cap plus we will get 14 times k cap cross j cap okay and the two times seven will be equal to zero because it is in same that is same thing that is k cap so from here we can say that i cap cross j cap will be equal to k cap okay so the answer will be 46 k cap and for i cap cross k cap will be equal to that is it in reverse direction so we can say it will be negative okay so i cap cross k cap will be equal to minus jcap, okay? plus 28, jcap cross i cap will also be in negative direction, so it will be equal to minus k -k -f.
03:27
And plus 49, now j -cap cross k -cab will be equal to i -cap, plus eight times k -cap cross i -calf will be equal to j -cab, because it is in our direction which we wanted.
03:40
So it will be positive.
03:42
And another is k -cap cross j -cab, which is in reverse direction...