The y-axis can be represented in vector form by

^

j

and −

^

j

Let

→

a

√ = √2

^

i

+

^

j

+

^

k

and

→

b

=

^

j

or −

^

j

cos θ =

^ a .b

^ |a| |b|

∴ cos θ =

(√2 ^ i + ^ j + ^ k ).(± ^ j )

|√2 ^ i + ^ j + ^ k || ^ j |

= ±

1×1

√(√2)2+(1)2+(1)2×√12

= ±

1

√4

= ±

1

2

So, the cosine of the angle which the vector
√2

^

i

+

^

j

+

^

k

makes with y axis is ±

1

2