Question

If → a = 4 ^ i + 7 ^ j − 5 ^ k and → b = 3 ^ i + 4 ^ j + ^ k find the direction cosines of → a − → b

Answer 1

Answer:

Therefore, the direction cosines of →a − →b are (1 / √46), (3 / √46), and (-6 / √46).

Step-by-step explanation:

Let →a = 4^i + 7^j − 5^k and →b = 3^i + 4^j + 1^k be two vectors.

Then, the vector →a − →b is given by subtracting the corresponding components of the two vectors:

→a − →b = (4^i + 7^j − 5^k) − (3^i + 4^j + 1^k)

= (4^i − 3^i) + (7^j − 4^j) − (5^k + 1^k)

= (4 − 3)^i + (7 − 4)^j − (5 + 1)^k

= 1^i + 3^j − 6^k

Now, to find the direction cosines of →a − →b, we need to divide each component by the magnitude of the vector:

|→a − →b| = √(1^2 + 3^2 + (-6)^2) = √46

The direction cosines are then given by:

cos α = (1 / √46)

cos β = (3 / √46)

cos γ = (-6 / √46)

Therefore, the direction cosines of →a − →b are (1 / √46), (3 / √46), and (-6 / √46).

To know more about the direction cosines refer:

https://brainly.in/question/54160971

https://brainly.in/question/5597386

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