Question 6 The distance from the origin to the plane passing through A and perpendicular to AB where 3i - Maths - Straight Lines

Question

Question 6 The distance from the origin to the plane passing
through A and perpendicular to AB where 3i + j + 2k, 5i - j + 3k
are the position vectors of A, B respectively is
(A) 1
(B) 2
(C) 3
(D) 4

Ghanshyam Dhakar · Accepted Answer

Dear student,
Given:position vector of Aa⇀=3i+j+2kposition vector of Bb⇀=5i-j+3know direction ratio of line AB5-3 ,-1-1,3-2
direction ratio of line AB 2,-2,1here,line AB is perpendicular to the plane
it means direction ratio of normal tothe plane will be same as direction ratio of line AB
we know general equation of plane:ax+by+cz=d where a,b and c are direction ratio of normal to the plane
put the values of direction ratio in above equation:2x-2y+z=d  
1this plane is passing through the point A3,1,2then, 2×3-2×1+2=dd=6 put this value in eq12x-2y+z=62x-2y+z-6=0so,the distance from origin0,0,0 to the  plane:d=ax1+by1+cz1+da2+b2+c2=0+0+0-622+-22+12d=63=2 answer
Regards

Question 6. The distance from the origin to the plane passing through A and perpendicular to AB where 3i + j + 2k, 5i - j + 3k are the position vectors of A, B respectively is (A) 1 (B) 2 (C) 3 (D) 4

Question 6. The distance from the origin to the plane passing through A and perpendicular to AB where 3i + j + 2k, 5i - j + 3k are the position vectors of A, B respectively is
(A) 1
(B) 2
(C) 3
(D) 4