Let P be a point not on the line L that passes through the points Q and R. The distance d from the point P to the line L is d = |a × b| |a| where a = QR and b = QP. Use the above formula to find the distance from the point to the given line. (0, 1, 1); x = 2t, y = 5 − 2t, z = 1 + t

Distance from point (0,1,1) to the given line is zero.

Step-by-step explanation:

Given parametric equations of line,

x=2t, y=5-2t, z=1+t

To find distance from (0,1,1), we have to eliminate t from above equations so that,

whose direction ratioes are (l,m,n)=(3,2,-2) and distance fro point (a,b,c)=(0,1,1) is given by,

Distance between point (0,1,1) and (1) is zero. That is point 90,1,1) is lies on the line (1).

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

false

step-by-step explanation: