With respect to the origin O, the lines l and m have vector equations r = 2i + k + λ(i − j + 2k) and r = 2j + 6k + µ(i + 2j − 2k) respectively. Find the equation of the...

With respect to the origin O, the lines l and m have vector equations r = 2i + k + λ(i − j + 2k) and r = 2j + 6k + µ(i + 2j − 2k) respectively. Find the equation of the...

find a.b if a=|10| and b=|2| , and the angle between a and b is -pi/3 radians.

Let a = (-2, -7, -1) |a|=

If not, when would linear dependency imply coplanarity?

shortest distance between two skew lines

I've tried to answer the problem but I'm pretty sure that everything I did was wrong. Here's the problem. This fun problem relates to physics. In case you’re not a physics major,...

A vehicle travels 25 km at an angle of 20 degrees north of east, then turns and travels a distance 35 km of at an angle of 50 degrees west of north and finally turns and travels a distance of 10 km...

Vectors in Three Dimensional Space In single variable calculus, or Calc 1 and 2, we have dealt with functions in two dimensions, or R2. In multivariable calculus, we will need to get accustomed to working in three dimensional space, or R3. Most of our notation and calculation will be the same, but with the extension of an added variable, z. The extended Cartesian graph now looks... read more