AP EAMCET Engineering 22 Apr 2019 Shift 1 Paper

a=2

^

i

+

^

j

+

^

k

b=

^

i

+2

^

j

−

^

k

Let, c=x

^

i

+y

^

j

+z

^

k

so,
c.a=0
This implies,
(x

^

i

+y

^

j

+z

^

k

).(2

^

i

+

^

j

+

^

k

)=0
2x+y+z=0 .....(I)
Since, a,b,c are coplanar so,
[

a

b

c

]=0
Therefore,
[

x	y	z
2	1	1
1	2	−1

]=0
x(−1−2)−y(−2−1)+z(4−1)=0
−3x+3y+3z=0
−x+y+z=0.....(II)
From equation (I) and (II),
x=0,y=−c
So,
x2+y2+z2=1
y=±

1

√2

This gives,
c=±

1

√2

(−

^

j

+

^

k

)