Vector Problems: Resultant Magnitude and Cross Product Calculations

[amanara]

Homework Statement

1. Two forces of equal magnitude are acting on a particle along two different directions. Let $$\theta$$
be the angle between them. If direction of one vector is reversed , the magnitude of resultant is halved. Find tan$$\theta$$.

2.The resultant of the two vectors having magnitudes 5 and 4 is 1. what is the magnitude of their cross product?

Homework Equations

The Attempt at a Solution

for 1st one-
tan$$\theta$$ = Acos$$\theta$$$$\frac{}{}$$A + Asin$$\theta$$
and tan2$$\theta$$ = 2Acos$$\theta$$$$\frac{}{}$$A + Asin$$\theta$$
2nd one -
i get cos$$\theta$$ as -1.

 

[lanedance]

i can't really work out what you have attempted, note that you can put a whole equation in the tex tags.

first if they are parallel, the resultant would go to zero when one is reversed
second, if they are pepindicular, the resultant would not change.

so you know the original angle is some where between 0 & pi/2

i would start by setting up a coordinate axis, where x is parallel to the vector that will be unchanged, then
$$F_x = F + F cos(\theta)$$
$$F_y = F sin(\theta)$$