Vectors: Find force needed to keep helicopter hovering if...

[spacejunkie]

I'm having trouble understanding the set up for this question.

Find the force needed to keep a helicopter hovering in place if the helicopter weighs 1000 pounds and a northeasterly wind exerts a force of 150 pounds.

The solutions manual says,

The unit vector in the northeasterly direction is <1/sqrt2, 1/sqrt2, 0>

Given that, I understand the rest of the solution. My question is how does one figure the unit vector to be <1/sqrt2, 1/sqrt2, 0> The z = 0 I get but the x and y allude me. Please help.

 

[skeeter]

the horizontal (with respect to the ground) force component is 150 lbs toward the northeast, or 150 lbs in a direction of 45 degrees

the unit vector for this component is 1 lb in the direction of 45 degrees ... the contributor to the solution manual broke this unit vector into x and y components with x as north and y as east.

x component = (1)cos(45) = 1/sqrt(2)
y component = (1)sin(45) = 1/sqrt(2)

 

[spacejunkie]

When I was trying to figure this out I kept using cos(45) as opposed to cos(pi/4) while in rad mode. Oops! Thanks again for your help! I'm off to refresh my knowledge on trigonometry and radian measure.

All the best,
The Spacejunkie