LINEAR ALGEBRA 3 Suppose that v and w are unit vectors in Rn

LINEAR ALGEBRA

3. Suppose that v and w are unit vectors in Rn satisfying v , w 0.3. Use properties of the dot product to find all values of c such that the angle between v - cw and v +2w is 90. V Cw and v

Solution

since vector v and w are unit vector

and also given that angel between

v-cw and v-2w is 90⁰

so taking dot product of these 2 vector

(v-cw).(v-2w)=|v-cw||v-2w|cos(90)

v²-2vw-cvw+2cw²=0 (cos(90)=0)

1-2-c+2c=0 (since v and w are unit vector)

c=1 (required result)