Let in a ABC, the length of the side AC be 6, the vertex B be (1,2,3) and the vertices A, C lie on the line x-63= y-72= z-7-2. Then the area (in sq. units) of ABC is:
(4) 21
A,C lie on the line, so the height from B is its distance from the line.
[figure]
P0(6,7,7), d=(3,2,-2), P0B=(-5,-5,-4)
P0B d=(18,-22,5) h= 833 17= 7 17 17=7
Area = 12 6 7=21
Answer: (4)
Let the line passing through the point (-1,2,1) and parallel to the line x-12= y+13= z4 intersect the line x+23= y-32= z-41 at the point P. Then the distance of P from the point Q(4,-5,1) is
Let P be the image of the point Q(7,-2,5) in the line L: x-12= y+13= z4 and R(5,p,q) be a point on L. Then the square of the area of PQR is .
Let P be the foot of the perpendicular from the point Q(10,-3,-1) on the line x-37= y-2-1= z+1-2. Then the area of the right angled triangle PQR, where R is the point (3,-2,1), is
If the square of the shortest distance between the lines x-21= y-12= z+3-3 and x+12= y+34= z+5-5 is mn, where m, n are coprime numbers, then m+n is equal to :
The distance of the line x-22= y-63= z-34 from the point (1,4,0) along the line x1= y-22= z+33 is :
Let L1: x-12= y-23= z-34 and L2: x-23= y-44= z-55 be two lines. Then which of the following points lies on the line of the shortest distance between L1 and L2 ?
Let L1: x-13= y-1-1= z+10 and L2: x-22= y0= z+4 , , be two lines, which intersect at the point B. If P is the foot of perpendicular from the point A(1,1,-1) on L2, then the value of 26 (PB)2 is .
Let a line pass through two distinct points P(-2,-1,3) and Q, and be parallel to the vector 3 i+2 j+2 k. If the distance of the point Q from the point R(1,3,3) is 5, then the square of the area of PQR is equal to :
The perpendicular distance, of the line x-12= y+2-1= z+32 from the point P(2,-10,1), is :