GUJCET 2020 Math Solved Paper

It is given that
‌

x+1

2

=‌

y

3

=‌

z−3

6

10x+2y−11z=3
Here the direction ratios of the line =(2,3,6)
Direction ratios of the normal to plane =(10,2,−11)
Angle between the line and the plane can be written as
sin−1(‌

a×a′+b×b′+c×c′

√a2+b2+c2√a′2+b′2+c′2

)
Where (a,b,c) are the direction ratios of a line and (a′,b′,c′) are the direction ratios of the normal to the plane
Substituting the values
=sin−1(‌

2×10+3×2+6×(−11)

√22+32+62√102+22+112

)
On further calculation
‌‌=sin−1(‌

20+6−66

7×15

)
‌‌=sin−1(‌

−40

7×15

)
So we get
=sin−1(−‌

8

21

)
By taking magnitude we get
=sin−1(‌

8

21

)