AP EAMCET Engineering 2011 Solved Paper

Let the vector v make an angle α with each of the three axes, then direction cosine of vare<cos‌α,cos‌α,cos‌α>
Also, cos2α+cos2α+cos2α=1
Hence, direction cosine of v are <

1

√3

,

1

√3

,

1

√3

> or <−

1

√3

,−

1

√3

,−

1

√3

>
So, the required line which makes equal angle with the coordinate axes is
v=±

1

√3

i±

1

√3

j±

1

√3

k
Now, the magnitude of the projection of the vector a=4i−3j+2j on line v.
∴ Projection of a along v=

a.v

|v|

=

3∕√3

1

=√3