CBSE Class 12 Math 2013 Solved Paper - Question 8 | ExamSiri

CBSE Class 12 Math 2013 Solved Paper

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Question : 8 of 29

Marks: +1, -0

a unit vector

a↖{→}

makes angle

π/3

with

i↖{\^}, π/4

with

j↖{\^}

and acute angle θ with

k↖{\^}

, then find the value of θ.

Solution:

Let

a↖{→}

=

xi↖{\^}+yj↖{\^}+zk↖{\^}

be the unit vector.
∴ x = cos

π/3

=

1/2

y = cos

π/4

=

1/√2

Now,

x^2+y^2+z^2

= 1
⇒

(1/2)^2+(1/√2)^2+z^2

= 1
⇒

z^2

= 1 -

1/4-1/2

=

1/4

⇒ z =

1/2

∴ cos θ =

1/2

⇒ θ =

π/3

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