Math, asked by taha4704, 17 hours ago

Find the vector of length 2 that makes an angle of π/4 with the positive x axis

Answers

Answered by pathakaaryan07
0

Answer:

Correct option is

C

2

i

2

j

+

2

k

Let

a

^

=li+mj+nk where l

2

+m

2

+n

2

=1

a makes an angle

4

π

with z-axis

∴n=

2

1

⇒l

2

+m

2

=

2

1

....(i)

then,

a

^

=li+mj+

2

k

Now,

a

^

+i+j=(l+1)i+(m+1)j+

2

k

...(ii)

Its magnitude is 1, hence

(l+1)

2

+(m+1)

2

=

2

1

...(ii)

From Eqs (i) and (ii) we get

2(l+m+1)=0

⇒(l+m)

2

=(−1)

2

l

2

+m

2

+2lm=1

⇒2lm=

2

1

⇒l=m=−

2

1

Hence,

a

^

=−

2

i

2

j

+

2

k

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