Question

Find a unit vector parallel to the resultant of the vectors
A=2i+3j+4k and B=3i -5j+k

Answer 1

Resultant Vector R is the Sum of vectors A and B
R = A + B
= ( 2i + 3j + 4k ) - ( 3i - 5j + k )
= 2i + 3j + 4k - 3i + 5j - k
= 2i - 3i + 3j - 3j + 4k - k
= -i + 0 j + 3k = - i + 3k
we know that
============
Full Vector = Unit Vector × Magnitude of Full Vector

=> Unit Vector = Full Vector / Magnitude of Full Vector
Now
magnitude of R =square root of ( ( - 1 ) square + 3 square ) = square root ( 1 + 9 ) = square root ( 10 )
Thus Unit vector along the direction of R
= Vector R / Magnitude of R
=( - i + 3k ) / sqaure Root ( 10 )

Answer 2

Answer:

Here is your answer.thank you.