Vector algebra help question pics are attachéd

Guess the question is too hard for the student room

posting the images sideways does not help

I've worked out the resultant force.

Since you have the resultant force, consider its horizontal components.

In order for the resultant of the horizontal forces with the tie cable to be zero, the additional force must be equal and opposite, which gives you the direction for the tie cable.

Can you take it from there?

yes I was working on that. But resultant has three components i j and k which one is the horizontal ?

Ps resultant force is (-940, 124,-31)

Since OP is 8k, then k is vertical, and the other two are horizontal (viz. a horizontal plane).

I assume your resultant is correct, not worked it through myself.

so the position would be (940,-124). I did get to that bit myself. But then I had no clue how to solve :/

Well that's the force required, and also the direction vector for the cable tie, but it's not the position. You're told the cable tie is at 45 degrees to the pole (presumably to the downward vertical), so you'll have to scale that to get the position.

The book doesn't agree. The answer for tension required is 1340n not 948n which is what we would get if we modulus the direction vector above (-940,124)

The cable tie is at 45 degrees to the horizontal as well. All you have there (presumably correctly) is the horizontal component of the force in the cable tie.

The cable tie is at 45 degrees to the horizontal as well. All you have there (presumably correctly) is the horizontal component of the force in the cable tie.

So divide by cos45 to get the total tension.

so now how would I find the position?

Sin45 as it's the angle to the downwards vertical, but it works out the same.

You have the direction.

Knowing the height of the pole and the angle of the tie you can work out how far away the cable tie will meet the ground.

Then, scale your direction vector appropriately.

still can't figure it out