00:01
Hello everyone we are going to understand this question here given in the question given weight value of weight that is 1500 newton value of f v which is given in the question f v is equal to 1 ,610 newton and value of f c which is given 2200 newton x x axis y axis and z axis value is given in the question and here it is given that this is y is negative means minus 6 and this x is minus x means minus 2 and z we have to find so we have to find value of z and x now we can write the vector of the given points means position of the given points with respect to origin so from the coordinates in the given coordinates in the diagram from the coordinates in the diagram in diagram we can write ab is equal to minus 2i minus 6 j plus 3k and value of ac means vector ac is equal to x i minus 6 j plus x k now we can write the value of vector a means force in the term of a b means force along to ab that will be sixteen hundred ten we are writing the value of force along to a b with respect to the means in direction or in vector form we can write vector ab upon mod a b vector ab upon mod ab so we can write sixteen hundred ten into minus two i minus six j plus three k upon magnitude of ab that is two square plus six square plus three square or we can write sixteen hundred ten upon seven because when we will solve this two square plus six square plus 3 squared that will give square root of 49 and square root of 49 is equal to 7.
03:25
So we can write minus 2i minus 6 j plus 3k or we can write after solving you will get 230 into minus 2i minus 6 j plus 3k.
03:52
Similarly we will find the magnitude of force or sorry, value of vector f ac means fourth in the term of in the vector form f ac is equal to f c into vector ac upon mod ac or we can write 2200 into value of ac that is x i minus 6 j plus z k upon square root of x square plus 36 plus z square.
04:47
So we can write f c is equal to 2200 into x i minus 6 j plus z k upon square root of x square plus 36 plus z square.
05:11
Now we will find the resultant.
05:15
R is equal to f -a force at the point a is equal to f -a plus f -a -b plus f -a -c.
05:41
So f -a is vertical force that is due to the weight.
05:46
So it will be minus 1 ,500 and it is allowed to z direction, so it will be minus 1 ,500.
05:54
Plus value of fab which we have calculated so we can write 230 into minus 2 i minus 6 j plus 3k plus f ac we have calculated 2200 into x i minus 6 j plus z k upon square root of x square plus 36 plus z square again we can write this like in this form means in i j and k term means we will we will take i term at one place j term at another place and k term on another place so we can write minus 460 minus 460 for taking i term so here 230 into 2 that is 460.
07:10
So here minus 460 plus 2200 into x because when we will multiply this term into x then it will be 2200 into x upon square root of x squared plus 36 plus z square into i plus we will take j term at one place.
07:40
So j term will give here minus 6 into minus 6 multiply by 230 minus 6 into 230 minus 6 into 230 minus sorry here minus 6 x into 2200 so it will it will be 2200 into 6 upon square root x squared plus 36 plus j squared multiply by j now similarly we will take k terms now we will take k terms at one place so here minus 1 ,500 plus 230 into 3 that will give 230 into 3 it means 690 or we can write 2200 2200 into z upon square root x squared plus 36 plus z squared into k now there is as we can say there is no support along to x -axis and along to z -axis so i term and k term will be zero as from the diagram from the diagram given in the question given in question there is no reaction force there is no reaction force along x -axis and z -axis so i term and k term will be equal to zero so we can write when we will put i term into equal to 0 then it will give minus 460 plus 2200 into x upon square root x square plus 36 plus z square equal to 0 so after solving we get we will get x upon x upon sorry x into 22 hundred upon 460 x x into 2200 upon 460 is equal to square root of x square plus 36 plus z square.
11:18
Again we can write 2200 .440.
11:27
After solving we will get 4 .78 into x is equal to square root of x square plus 36 plus z square.
11:44
Now we will square both sides then we will get 22 .85 x square is equal to x square plus 36 plus z square.
12:01
Let this is equation one.
12:04
Now similarly we will put k term 0 then minus 50 ,500 plus 619 plus 2200 into z upon square root of x square plus 36 plus z squared equal to 0 again we will solve it or we will calculate the given terms so here it will be 2200 2200 .10 into z is equal to square root of x squared plus z squared plus 316.
12:58
This is 36.
13:05
Again, we can write 7 .34.
13:11
Z is equal to x square, 7 .34.
13:18
Z square is equal to x square plus z square plus 360 because here 20 to 100 10 it will give 2 .71 so when we will take square then it will give 7 .34 z square is equal to x square plus z square plus 360 again we can write z square is equal to z square is equal to x square plus 36 sorry it's not a 360 it's a 36 x square plus 36 and where z square will take right side then it will give 6 .34 again we can let this is equation 2 that this is equation 2 now from equation 1 and 2 from equation 1 and 2 we can write 22 .8 x square minus x square is equal to 36 plus x square plus 36 upon 6 .34.
14:51
Again we can write 21 .85 into x square is equal to 36 plus x square upon 6 .34, sorry, x square upon 6 .34 plus 36 upon 6 .34.
15:24
Again we can write 6 .34.
15:34
This is 34, not 30...