Question

If the resultant of the vectors 3i^+4j^+5k^ and which 5i^+3j^+4k^ makes an angle with x - axis,then find cos

Answer 1

Answer:

Cos(α) = 47 / 50

Step-by-step explanation:

Let angle between first vector and second vector is α

First vector = u = 3i + 4j + 5k

Second vector = v = 5i + 3j + 4k

We know that

Dot product of vectors u and v is given as

u · v = ║u║║v║Cos(α)

And this implies

Cos(α) = ( u · v ) / ( ║u║║v║ )

And

u · v = ( 3i + 4j + 5k ) · ( 5i + 3j + 4k ) = 15 + 12 + 20 = 47 units

And

║u║ = √(3² + 4² + 5²) = √(9 + 16 + 25) = √50

║v║ = √(5² + 3² + 4²) = √(25 + 9 + 16) = √50

So

║u║║v║ = √50×√50 = 50

By putting all values in the above formula of dot product we get

Cos(α) = 47 / 50