Related InterviewSolutions

• `vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3)` The position vector of L, the foot of the perpendicular from P on the line `vec(r)=vec(a)+lamdavec(b)` is -A. `6hat(i)+7hat(j)+7hat(k)`B. `3hat(i)+2hat(j)-2hat(k)`C. `3hat(i)+5hat(j)+9hat(k)`D. `9hat(i)+9hat(j)+5hat(k)`
• `vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3)` If A is the point with position vector `vec(a)` then area of the `DeltaPLA` in square units is equal to -A. `3sqrt(6)`B. `7sqrt((17)/(2))`C. `sqrt(17)`D. `(7)/(2)`
• State which of the following statement is true ?A. The line koining the points (1,2,3) and (1,5,3) makes angle `(pi)/(2)` with the positive y-axis.B. The line joining the points (1,-1,0) and (2,-1,0) is parallel with the positive x-axis.C. The angle between the lines `(x-5)/(7)=(y+2)/(-5)=(z-2)/(1)` and `(x-1)/(1)=(y)/(2)=(z-1)/(3)` is `(pi)/(3)`D. The anlge between the lines `2x=3y=-z` and `6x=-y=-4z` is `(pi)/(4)`.
• The equation of a line passing through the points (5,2,7) and paraleel to y - axis is -A. `(x-5)/(b)=(y-2)/(0)=(z-7)/(b),bne0`B. `(x+5)/(b)=(y+2)/(0)=(z+7)/(b),bne0`C. `(x-5)/(0)=(y-2)/(b)=(z-7)/(0),bne0`D. `(x+5)/(0)=(y+2)/(b)=(z+7)/(b),bne0`
• State which of the following statement is true ?A. The line `(x-x_(1))/(a)=(y-y_(1))/(b)=(z-z_(1))/(c)` is parellel to x-axis, is `ane0` and `b=c=0` is satisfied.B. The line `(x-x_(1))/(a)=(y-y_(1))/(b)=(z-z_(1))/(c)` is passing through the origin, if `(x_(1))/(a)=(y_(1))/(b)=-(z_(1))/(c)` is satisfied.C. The vector equation of a line passing through the points (1,0,0) and (0,5,0) is given by `vec(r)=hat(i)+t(-hat(i)-5hat(j)+3hat(k))`D. The line `x=3+2t,y=5,z=3` is parallel to y-axis.
• The equation of a line passing through the points (1,2,3) and (4,0,6) is -A. `(x-1)/(4)=(y-2)/(0)=(z-3)/(6)`B. `(x-4)/(1)=(y-0)/(2)=(z-6)/(3)`C. `(x-1)/(-3)=(y-2)/(2)=(z-3)/(-3)`D. `(x-4)/(3)=(y-0)/(-2)=(z-6)/(3)`
• The equation of a line passing through the points (1,2,3) and (4,5,6) is given by -A. `(x-1)/(1-4)=(y-2)/(2-5)=(z-3)/(3-6)`B. `(x-1)/(4-1)=(y-2)/(5-2)=(z-3)/(4-2)`C. `(x-4)/(4-1)=(y-5)/(5-2)=(z-6)/(5-3)`D. `(x-4)/(4-1)=(y-5)/(2-5)=(z-6)/(3-6)`
• The angle between the straight lines `x=5,y=4t+5,z=4t+3` and `(x-5)/(5)=(y-6)/(0)=(z-(1)/(2))/(0)` is-A. `(pi)/(2)`B. `(pi)/(3)`C. `(pi)/(4)`D. 0
• The angle between the straight lines `(x-4)/(2)=(y-5)/(0)=(z-6)/(0)` and `(3-x)/(3)=(y-7)/(0)=(z-3)/(0)` is -A. `pi`B. `(pi)/(2)`C. `(pi)/(3)`D. `(pi)/(6)`
• `L_(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L_(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2)` The lines `L_(1)` and `L_(2)` intersect at the pointA. (-3,2,1)B. (2,1,-3)C. (1,-3,2)D. none of these