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Find the foot of the perpendicular drawn...

Find the foot of the perpendicular drawn from the point `(2 hati - hatj + 5hatk)` to the line `vec r= (11hati - 2 hatj - 8hatk)+t(10 hat i-4 hatj - 11hatk)`. Find also the length of the perpendicular.

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Find the foot of the perpendicular drawn from the point (2hat(i)-hat(j)+5hat(k)) to the line vec(r)=(11hat(i)-2hat(j)-8hat(k))+t(10hat(i)-4hat(j)-11hat(k)) . Find also the length of the perpendicular.

Find the equation of the plane which passing through the point hati + hatj + hatk and parallel to the plane vec r.(2hati - hatj + 2hatk) = 0.

Find the distance of the point with position vector 2 hati+ hatj- hatk from the plane vecr .( hati- 2 hatj+ 4 hatk)=9 .

Find the equation of the plane which passing through the points hati+ hatj+ hatk and parallel to the plane vecr.(2 hati-hatj+2 hatk)=5

find the projection of the vector hati-3hatj-7hatk on the vector 7hati-hatj-8 hatk

Find a unit vector which is perpendicular to both vecA = 3hati + hatj + 2hatk and vecB = 2hati - 2hatj + 4hatk .

Vectors Perpendicular to hati - hatj- hatk and in the plane of hati + hatj + hatk and - hati + hatj + hatk are

Find the projection of the vector hati+3hatj+7hatk on the vector 7hati-hatj+8hatk .

Find the vector equation of the plane that contains the lines vec r=(hati+hatj)+lambda(hati+2hatj-hatk) and vec r=(hati+hatj)+mu(-hati+hatj-2hatk) .Also find the length of the perpendicular drawn from the point (2,1,4) to the plane thus obtained.

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