The number of values of 
(0, 
) for which the system of linear equations x+3y+7z=0, −x+4y+7z=0, (sin 3
) x +(cos 2
) y+2z=0 has a non-trivial solution, is :
(a)
One
(b)
Three
(c)
Four
(d)
Two
The number of values of (0, ) for which the system of linear equations x+3y+7z=0, −x+4y+7z=0, (sin 3) x +(cos 2) y+2z=0 has a non-trivial solution, is :
(a)
One
(b)
Three
(c)
Four
(d)
Two
Question ID - 56910 | SaraNextGen Top Answer
The number of values of (0, ) for which the system of linear equations x+3y+7z=0, −x+4y+7z=0, (sin 3) x +(cos 2) y+2z=0 has a non-trivial solution, is :
(a)
One
(b)
Three
(c)
Four
(d)
Two
|
The number of values of |
|||
|
(a) |
One |
(b) |
Three |
|
(c) |
Four |
(d) |
Two |
1 Answer
127 votes
Answer Key / Explanation : (d) -
(8−7 cos 2
) −3(−2−7sin3
)+7(−cos 2
−4 sin 3
)=0
14−7 cos 2
+21 sin 3
−7 cos 2
−28 sin 3
=0
14−7 sin 3
−14 cos 2
=0
14−7(3 sin
−4sin3
) −14(1−2 sin2
)= 0
−21 sin
+28 sin3
+28 sin2
=0
7 sin 
[−3+4 sin2
+ 4 sin 
]=0
Sin 
,
4 sin2
+6 sin 
−3=0
2 sin 
(2 sin 
+3) −1(2 sin 
+3)=0
Sin 
=
sin
Hence, 2 solutions in (0, 
)
Option (d)
127 votes
Answer Link
127