IIT JEE , AIEEE Forum - Mathematics , Vectors - is vectors a b clie along diffrent axis then value of sina+sinB+sinc is_ if a b c are ang

shinee

i have thought a different method
i have assumed that the vector A subtends the angle a with positive x axis, vector (and 90-a with positive y axis and it lies only in xy plane)
vector B makes an angle of b with positive y xais and it lies completly in yz plane and the vector C too lies completly in the yz plane making an angle of c with positive z xais
as the total angle between the y and z axes is 90, let us assume that the angle between the vectors C and B to be 90-(b+c)
the y component of vector a is Asina and the x component is Acosa
now taking the component of vector Asina along the vector B, we get, Asinacosb and the other component of vector Asina is Asinasinb and it lies along yz palne making an angle 90 with vector B
i have found out the resultant of B and C considering the angle between them as 90-(b+c)
then after finding their resultant , i have found the resultant of this with Acosa
then considering this whole resultant , i taken found out the angles with positive x, y, z axes and cos^2@+cos^#+cos^2$=1
where @,#,$ are the angles of this resultant with x,y,z axes
then we get the equation of the form
B^2cos^c+c^2sin^2c=-2BCsinccosb.................................1
and similarly after taking Asinasinb and C,
we get 2C=A(sinasin^2b)(sin^2c-sin^2b)/[sin^2bsinc+cos^2bcosc-2cosbsinb(sinc+cosc)......2
and after considering Asinacosb with C,
we get 2C=A(sinacosbsinb-1)/cosb(cosc-1)...............3
solving 1, 2 and 3, we get the value of sina, sinb,sinc
add them to get the soln
actually i have gtg
i will post the ans tomorrow

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