Related InterviewSolutions

• The distance between the line `x=2+t,y=1+t,z=-1/2-t/2` and the plane `vecr.(hati+2hatj+6hatk)=10`, isA. `1/6`B. `1/(sqrt(41))`C. `1/7`D. `9/(sqrt(41))`
• A line with directional cosines prontional to `2, 1,2` meets each of the lines `x = y + a = z and x+ a = 2y = 2z`. The coordinates of each of the points deintersection are given byA. `(2a,3a,a),(2a,a,a)`B. `(3a,2a,3a),(a,a,a)`C. `(3a,2a,3a),(a,a,2a)`D. `(3a,3a,3a),(a,a,a)`
• The shortest distance between the lines `2x + y + z - 1 = 0 = 3x + y + 2z - 2` and `x = y = z`, isA. `1/(sqrt(2))`B. `sqrt(2)`C. `3/(sqrt(2))`D. `(sqrt(3))/2`
• Find the vector equation of the plane in which the lines `vecr=hati+hatj+lambda(hati+2hatj-hatk)` and `vecr=(hati+hatj)+mu(-hati+hatj-2hatk)` lie.A. ` vecr.(2hati+hatj-3hatk)=-4`B. `vecrxx(-hati+hatj+hatk)=vec0`C. `vecr.(-hati+hatj+hatk)=0`D. none of these
• Find the vector equation of the plane in which the lines `vecr=hati+hatj+lambda(hati+2hatj-hatk)` and `vecr=(hati+hatj)+mu(-hati+hatj-2hatk)` lie.A. `vecr.(hati+hatj+hatk)=0`B. `vecr.(-hati+hatj+hatk)=0`C. `vecr.(-hati+hatj+hatk)=1`D. `vecr.(hati+hatk-hatk)=0`
• The angle between the lines `vecr=(hati+hatj+hatk)+lamda(hati+hatj+2hatk)` and `vecr=(hati+hatj+hatk)+mu{(-sqrt(3)-1)hati+(sqrt(3)-1)hatj+4hatk}` isA. `(pi)/6`B. `(pi)/4`C. `(pi)/3`D. `(2pi)/3`
• The equation of the plane contaiing the lines `vecr=veca_(1)+lamda vecb` and `vecr=veca_(2)+muvecb` isA. `[(vecr, veca, vecb)]=0`B. `[(vecr,veca,vecb)]=veca.vecb`C. `[(veca,vecb,veca)]=veca.vecb`D. none of these
• The shortest distance between the lines `vecr=(hati-hatj)+lamda(hati+2hatj-3hatk)` and `vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk)` isA. `6`B. `6/(sqrt(5))`C. `3/(sqrt(5))`D. `2/(sqrt(5))`
• the lines `(x-2)/1` = `(y-3)/1` = `(z-4)/-k` and `(x-1)/k` = `(y-4)/1` = `(z-5)/1` are coplanar if k=?A. `k=3` or `-3`B. `k=0` or `-1`C. `k=1` or `-1`D. `k=0` or `-3`
• Two lines `L_1x=5, y/(3-alpha)=z/(-2)a n dL_2: x=alphay/(-1)=z/(2-alpha)`are coplanar. Then `alpha`can take value (s)a. `1`b. `2`c. `3`d. `4`A. 1,4,5B. 1,2,5C. 3,4,5D. 2,4,5