Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

The unit vector in ZOX - plane and making angle 45° and 60°, respectively with a=2i+2j-k and b=0i+j-k is?

1) (-1/√2)i+(1/√2)k

2) (1/√2)i-(1/√2)k

3) (1/3√2)i+(4/3√2)j+(1/3√2)k

4) None of these

Answer: (2) (1/√2)i-(1/√2)k

Solution: Say, c = xi+yk

|c| = √(x2+y2) = 1

a2+b2 = 1

Now, a and c are inclined at 45 degrees

c.a = |c||a|cos 45

Cos 45 = 2x-y/√(4+4+1)

2x-y = 3/√2 …………(1)

Again, b and c are inclined at 60 degrees

c.b = |c| |b| cos 60

Cos 60 = -y/√2

y=-1/√2 ………….(2)

Now putting the value of y in equation (1), we get;

x = 1/√2

Therefore, the required unit vector is (1/√2)i-(1/√2)k

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