AP EAPCET 23-Aug-2021 Shift 1 Paper

Given, planes are 2x−y+z=6 and x+y+2z=3
General equation of plane is ax+by+cz=d
Normal vector of plane is a

^

i

+b

^

j

+c

^

k

.
For plane 2x−y+z=6
n1=2

^

i

−

^

j

+

^

k

For plane x+y+2z=3
n2=

^

i

+

^

j

+2

^

k

Angle between n1 and n2 is given as,
cos‌θ=

|n1.n2|

|n1||n2|

=

(2−1+2)

√4+1+1√1+1+4

=

3

6

=

1

2

cos‌θ=cos‌

π

3

∴ Angle between given planes is

π

3

.