Find the equation of plane which is a...

Find the equation of plane which is at a distance `4/(sqrt(14))` from the origin and is normal to vector `2 hat i+ hat j-3 hat kdot`

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©answer any one question: (i) find the vector equation of the plane at a distance 6/(sqrt29) unit from the origin and perpendicular to the vector 2 hat i -3 hat j+ 4 hat k . Also convert this equation in cartesian form.

Find the direction cosines of the vector hat i+2 hat j+3 hat kdot

Find the equation of the sphere described on the joint of points Aa n dB having position vectors 2 hat i+6 hat j-7 hat ka n d-2 hat i+4 hat j-3 hat k , respectively, as the diameter. Find the center and the radius of the sphere.

Find the vector equation of the plane passing through the points having position vectors hat i+ hat j-2 hat k ,2 i - hat j+ hat ka n d hat i+2 hat j+ hat kdot

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 ).

Find the equation the plane which contain the line of intersection of the planes vec rdot( hat i+2 hat j+3 hat k)-4=0a n d vec rdot(2 hat i+ hat j- hat k)+5=0 and which is perpendicular to the plane vec r(5 hat i+3 hat j-6 hat k)+8=0 .

find the projection of 3hat i - hat j + 4hat k on 2 hat i + 3 hat j -6 hat k

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 .

Find the vector equation of a line which passes through the point with position vector hat(i)-2hat(j)+4hat(k) and is in the direction of hat(i)+2hat(j)-hat(k) . Also, reduce it to cartesian from.

Find the equation of the plane passing through (3,4,-1), which is parallel to the plane vec rdot(2 hat i-3 hat j+5 hat k)+7=0.

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