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[" 925) Show that the points "(i-j+3k)" ...

[" 925) Show that the points "(i-j+3k)" and "3(i+j+i)" are equidiation from the plare "],[qquad vec r*(5vec i+2j-7hat k)+9=0" and lies on opposite side of it."],[[" Astume that each bom child to equally likely to be a boy "," is a "," is "," is "]]

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Show that the points hat i-hat j+3hat k and 3(hat i+hat j+hat k) are equidistant from the plane vec r*(5hat i+2hat j+hat k)+9=0 and lie on opposite sides of it.

Show that the points hat i- hat j+3 hat ka n d3( hat i+ hat j+ hat k) are equidistant from the plane vec rdot(5 hat i+2 hat j+ hat k)+9=0 and lie on opposite sides of it.

Find the distance of the point (33,3) from the plane vec r*(5hat i+2hat j-7hat k)+9=0

Show that the line of intersection of the planes vec r*(hat i+2hat j+3hat k)=0 and vec r=(3hat i+2hat j+hat k)=0 is equally inclined to i and k. Also find the angle it makes with j.

The coordinates of the point where the line vec(r)=(6i-j-3k)+t(-i+4k)" meets the plane "vec(r)*(hat(i)+hat(j)-hat(k))=3 are

If vec a = hat i +2 hat j +hat k, vec b= 3 hat i +2 hat j- 7hat k and vec c = 5 hat i +6 hat j -5hat k . show that vec a, vec b and vec c are coplanar.

if |vec C|^(2)=60 and vec Cx(hat i+2hat j+5hat k)=0 then a value of vec C*(-7hat i+2hat j3+hat k) is

If vec a=5 hat i-hat j-3 hat k and vec b=hat i+3 hat j -5 hat k , then show that the vecctors vec a+vec b and vec a-vec b are perpendicular.

If vec a=5hat i-hat j-3hat k and vec b=hat i+3hat j-5hat k then show that the vectors vec a+vec b and vec a-vec b are orthogonal.

Find the distance of the point (-1,-5,-10), from the point of intersection of the line vec r=(2hat i-hat j+2k)+lambda(3hat i+4hat j+2hat k) and the plane vec r.(hat i-hat j+hat k)=5