Find the equation of the plane perpendicular to the line (x-1)/2=(y... 02:37 Find the equation of the plane through the points (2,2,1) and (9,3,6) ... 04:50 The equation of the plane containing the two lines (x-1)/2=(y+1)/(-1... 03:39 The direction ratios of the...
解析 x+y=2. The direction vectors of the lines are (1,-1,2) and (-1,1,0), so a normal vector for the plane is(-1,1,0)* (1,-1,2)=(2,2,0) and it contains the point (2,0,2). Then an equation of the plane is 2(x-2)+2(y-0)+0(z-2)=0⇔ x+y=2....
Find the shortest distance between the given line →r=(λ−1)ˆi+(λ+1)ˆj+(λ+1)ˆk vec(r ) =(1−μ)ˆi+(2μ−1)ˆj+(μ+2)ˆk. View Solution Find the vector and Cartesian equations of the plane containing the two lines→r=2ˆi+ˆj−3ˆk+λ(ˆi...
1.) Find the equation of the plane that contains both lines. Equation of a Plane: Recall that if we have a point {eq}(x_0,y_0,z_0) {/eq} in a plane and a normal to the plane {eq}\vec n = \left {/eq}...
Find the equation of a plane containing P_0=(1,2,3) and perpendicular to n=[1,-1,2] . Solution: (x-1)-(y-2)+2(z-3)=0\Rightarrow x-y+2z=5 3.3 The line of intersection of two planes Example Find a vector tangent to the line of intersection of the planes Solution: We ...
Find the equation of the plane containing the points {eq}(1,1,1){/eq} and {eq}(3,0,4){/eq} and the vector {eq}\left \langle 1,1,-1 \right \rangle{/eq} Equation of Tangent Line: If {eq}x=x(t) {/eq} and {eq}y=y(t) {/eq} are parametriz...
Give an equation of the plane that contains the line x=t,y−2+3t, and z=5−t and lies parallel to the plane 2x−y+4z=12. Equation of a Plane: The elements that make up a plane are the point and the normal vector. Tw...
The lines ~r1(t) = h0; 1; 1i + th1; 1; 2i and ~r2(s) = h2; 0; 3i + sh1; 4; 4i intersect at the point h3; 4; 7i when s = 1 and t = 3. Find an equation of the plane that contains these ...
Q. Show that the line of intersection of the planes x+2y+3z=8 and 2x+3y+4z=11 is coplanar with the line x+11=y+12=z+13. Also find the equation of the plane containing them. Q. Find the equation of the plane through the line of intersection of the planes 2x+y−z=3,5x−...
Find the equation of the plane containing the line2x+y+z−1=0,x+2y−z=4and at a distance of1√6from the point (2,1,-1). View Solution Find the shortest distance between the linesx−2−1=y−52=z−03andx−02=y+1−1=z−12. ...