Question

Find a unit vector in the direction of i-j+3k,2i+j-2k & -i-j-3k

Answer 1

Hint:

Let "vector r" = a î + b j + c k
So, unit vector in the direction of "vector r"
Until vector in the direction of "vector r" = ± ("vector r"/magnitude of "vector r" )
= ± ("vector r"/ |"vector r"|)
= ± ( a î + b j + c k )/|a î + b j + c k|
= ± ( a î + b j + c k )/|(a² + b² + c²)½|
Now solve it.

Solution:

According to your question:

"i-j+3k"
Until vector = ± [(i-j+3k)/(1² + (-1)² + 3²)½]
= ± [(i-j+3k)/√11]
= ± [(1/√11) i -(1/√11) j + (3/√11) k]

Similarly,
"2i+j-2k"
Until vector = ± [(2i+j-2k)/(2² + 1² + (-2)²)½]
= ± [(2i+j-2k)/√9]
= ± [(2i+j-2k)/3]
= ± [(2/3) i + (1/3) j + (2/3) k]

"-i-j-3k"
(On solving this, we get)
Unit vector =
= ± [(-1/√11) î + (-1/√11) j + (-3/√11) k]

Thankyou!!!