Introduction:
In this question, we are given two vectors A and B, and we have to find the resultant vector R. We are also asked to find the direction and magnitude of R.

Finding R:
To find the resultant vector R, we can use the formula R = A + B. Substituting the given values, we get:

R = A + B
R = (2i - 6j - 3k) + (4i + 3j - k)
R = 6i - 3j - 4k

Therefore, the resultant vector R is 6i - 3j - 4k.

Direction of R:
To find the direction of R, we need to calculate the unit vector of R. The unit vector of R is the vector in the direction of R with a magnitude of 1.

We know that the magnitude of R is given by the formula:

|R| = sqrt(Rx^2 + Ry^2 + Rz^2)

Substituting the values of R, we get:

|R| = sqrt((6)^2 + (-3)^2 + (-4)^2)
|R| = sqrt(61)

Therefore, the magnitude of R is sqrt(61).

Now, to find the unit vector of R, we divide R by its magnitude as follows:

R/|R| = (6i - 3j - 4k)/sqrt(61)

Therefore, the unit vector of R is (6i - 3j - 4k)/sqrt(61).

Magnitude of R:
We have already calculated the magnitude of R in the previous step, which is sqrt(61).

Conclusion:
In this question, we have found the resultant vector R by adding vectors A and B. We have also found the direction and magnitude of R.

No I can't answer this
I am sorry