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Find the length of the perpendicular drawn from the point`(5,4,-1)` to the line ` vec r= hat i+lambda(2 hat i+9 hat j+5 hat k),` wher `lambda` is a parameter.

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Find the length of the perpendicular drawn from the point (5,4,-1) to the line vec(r)=hat(i)+t(2hat(i)+9hat(j)+5hat(k))

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Find the equation of the plane which is parallel to the lines vec r= hat i+ hat j+lambda(2 hat i+ hat j+4 hat k)a n d(x+1)/(-3)=(y-3)/2=(z+2)/1"" and is passing through the point (0,1,-1 ).

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Find the unit vector perpendicular to the plane vec r.(2 hat i+ hat j+2 hat k)=5.

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Find the vector of length 3 unit which is perpendicular to hat i+ hat j+ hat k and lies in the plane of hat i+ hat j+ hat k and 2 hat i-3 hat j .

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