my teacher gave me this problems but i just can't figure out this one, please i really need to know this and if you can post Steps on how to do it will be awesome. Also i would rather see the procedure than a lot of explanation.
Given u=<3,4> w=<-2,2> and v=<-5,6> find the following:
u + v_____v - u_____4u - 3v_____||4u - 3v||
Also:
a unit vector in the direction of v
find the direction angle for -u
v*w (is v times w)
find the angle between v and w
show that the standard unit vectors i and j are orthogonal.
I know this long but i hope someone knows this answers, this is not homework to get points, I'm studying for a college test.
Just add the x and y components of each vector together.
Subtract the corresponding x and y components:v - u_____
Multiply each vector by the corresponding scalar coefficient, and then subtract them:4u - 3v_____
Since we have , apply the equation to find the norm of the vector:||4u - 3v||
first findAlso:
a unit vector in the direction of v
Thus, the unit vector is
I'll get back to this one. Is the angle supposed to be measured with respect to the x axis? I want to say that the angle would be ...find the direction angle for -u
I'm assuming you mean find the dot product?v*w (is v times w)
When you take the dot product, you're left with a scalar value. You need to multiply the corresponding x and y components together and then add what you have left over:
The equation for finding the angle between two vectors is this :find the angle between v and w
Thus,
To show that two vectors are orthogonal, you need show that the dot products of the two vectors is zero.show that the standard unit vectors i and j are orthogonal.
I hope this helps!
--Chris