Question

p= i-2j+2k and Q=3i-j+k. find the vector which when added to ( P-Q) will give a unit vector along the z-axis​

Answer 1

Answer:

Let required vector be a

i

∧

+b

j

∧

+c

k

∧

∵ It makes equal angle with x and y-axis.

⟹

a

2

+b

2

+c

2

a

=

a

2

+b

2

+c

2

b

⟹a=b

∵It is a unit vector.

⟹a

2

+b

2

+c

2

=1−(i)

and it is orthogonal to −

i

∧

+2

j

∧

+2

k

∧

⟹−a+2b+2c=0

∵a=b

⟹−a+2a+2c=0

⟹2c=−a

⟹c=

2

−a

Puttingb=a,c=

2

−a

in(i):

⟹a

2

+a

2

+

4

a

2

=1

⟹4a

2

+4a

2

+a

2

=4

⟹9a

2

=4

⟹a=±

3

2

∴a

i

∧

+b

j

∧

+c

k

∧

=a

i

∧

+a

j

∧

+

2

−a

k

∧

=±

3

1

(2

i

∧

+2

j

∧

−

k

∧

)