00:01
In this problem we have given vector a has magnitude 5 meters and its direction is 30 degree east of north so we know that this is east this is west north and south so vector a has magnitude 5 meter and direction is 30 degree east of north so that means this angle is 30 degree and this vector has magnitude 5 meter right and vector b has magnitude 6 meters its direction is 60 degrees south of west 60 degree south of west that means this is the vector b and it has magnitude 6 meter okay this is vector a and this is vector b now we have given vector c has magnitude 4 meters and direction is due west so this is vector c magnitude is 4 meter direction towards west now in part a we have to sketch the three vectors so this is answer for part a now in part b we have to find the components of all three vectors if the x -axis point due east so suppose this is x -axis and y -axis points due north so this is y -axis we have to find the component so we can write vector a in the form of component so we know that the x component of this vector will be this and this angle will be 60 degree so we can write the x component of this vector magnitude of vector a into cos of 60 in i -cap direction plus magnitude of vector a sine 60 j cap direction so it is given 5 meter so this is 5 cost 60 i cap plus 5 5 sine 60 j cap so this is equal to 2 .5 i cap plus 5 sine 60 so 5 sine 60 will be equal to 4 .3 so we can find this is x component and this is y component now for vector b we can write vector b as x component will be 6 cost 60 and the negative x x xx is so this will be minus 6 cost 60 i cap and it has negative y component also this will be 6 sine 60 j cap so we can say this will be equal to minus 3 i cap and minus 6 into sin 60 that is equal to minus 5 .2 j cab okay so this is the vector b in component form x component is minus 3 and y component is minus 5 .2 meter now vector c is 4 meter due west so we can write this will be minus 4 i there.
04:16
That means x component of vector c is minus 4 this minus sign because it is in towards negative x -axis now this is the answer for part b now in part c we have to find the component of all three vectors if the x axis point 60 degree north of east 60 degree north of east suppose this is east, this is west, this is north and this is south.
04:55
So in this case, first we have given that the x axis points 60 degree north of east.
05:11
This is x -axis, okay, this is negative x -axis, and y -axis points 60 degree west of north.
05:36
60 degree west of north.
05:43
So this will be the y -axis.
05:48
This is positive y and this is negative y.
05:56
Okay.
05:57
So now we have x -axis and y -axis in this direction.
06:02
So we can see that vector a, now vector a will be in the direction of positive x -axis, which will be 5 y -cap...