Math241 D1 Quiz#1 June 15, 2011
Name: Solutions
1.[6pts] Let −→
aand −→
bbe two vectors in R3. If |−→
a|= 3 and |−→
b|=√5 and the angle
between −→
aand −→
bis π
3then find −→
a·−→
b.
Sol) −→
a·−→
b=|−→
a||−→
b|cos(θ) = 3√5 cos( π
3) = 3√5×1
2.
2.[7pts] Find a unit vector that has the same direction as the vector. −→
a=−→
i−2−→
j+2−→
k
The components of the vector are called the direction cosines.
Sol) −→
a
|−→
a|.
3.[7pts] Find the distance from a point P(1,2,4) to the (1)x−axis and (2)xy−plane.
Sol) (1) Let Q= (1,0,0). The distance is |P Q|.
(2) The height is 4. Or let R= (1,2,0). Take the distance |P R|.