Let A be a point on the line `vec(r)=(1-3mu)hati+(mu-1)hatj+(2+5mu)hatk` and `B(3,2,6)` be a point in the space. Then the value of `mu` for which the vector `vec(AB)` is parallel to the plane `x-4y+3z=1` is: (a) `1/8` (b) `1/2` (c) `1/4` (d) `-1/4`A. `(1)/(4)`B. `-(1)/(4)`C. `(1)/(8)`D. `(1)/(2)`

Let A be a point on the line `vec(r)=(1-3mu)hati+(mu-1)hatj+(2+5mu)hat

1.	Let A be a point on the line `vec(r)=(1-3mu)hati+(mu-1)hatj+(2+5mu)hatk` and `B(3,2,6)` be a point in the space. Then the value of `mu` for which the vector `vec(AB)` is parallel to the plane `x-4y+3z=1` is: (a) `1/8` (b) `1/2` (c) `1/4` (d) `-1/4`A. `(1)/(4)`B. `-(1)/(4)`C. `(1)/(8)`D. `(1)/(2)`
Answer» Correct Answer - A Given equation of line is `r=(1-3mu)hati+(mu-1)hatj+(2+5mu)hatk` Clearly, any point on the above line is of the form `(1-3mu,mu-1,2+5mu)` Let A be `(-3mu+1,mu-1,5mu+2)` for some `muinR.` Then, `AB(3-(-3mu+1))hati+(2-(mu-1))hatj` `+(6-(5mu+2))hatk[becauseAB=OB-OA]` `=(3mu+2)hati+(3-mu)hatj+(4-5mu)hatk" "...(i)` Normal vector (n) of the plane `x-4y+3z=1` is `n=hati-4hatj+3hatk" "...(ii)` `because`AB is parallel to the plane. `:.` n is perpendicular to the AB. `impliesAB.n=0` `implies[(3mu+2)hati+(3-mu)hatj+(4-5mu)hatk].[hati-4hatj+3hatk]=0` [From Eqs. (i) and (ii)] `implies(3mu+2)-4(3-mu)+3(4-5mu)=0` `implies" "-8mu+2=0` `implies" "mu=(1)/(4)`

Discussion

No Comment Found

Related InterviewSolutions

Read the following passage and answer the questions. Consider the lines `L_(1):(x+1)/(3)=(y+2)/(1)=(z+1)/(2),L_(2):(x-2)/(1)=(y+2)/(2)=(z-3)/(3)` The distance of the point (1,1,1) from the plane passing throught the point (-1,-2,-1) and whose normal is perpendicular to both the lines `L_(1)` and `L_(2)`, isA. `2//sqrt(75)` unitB. `7//sqrt(75)` unitsC. `13//sqrt(75)` unitsD. `23//sqrt(75)` units
Read the following passage and answer the questions. Consider the lines `L_(1):(x+1)/(3)=(y+2)/(1)=(z+1)/(2),L_(2):(x-2)/(1)=(y+2)/(2)=(z-3)/(3)` The unit vector perpendicualr to both `L_(1)` and `L_(2)` isA. `(-hati+7hatj+7hatk)/(sqrt(99))`B. `(-hati-7hatj+5hatk)/(5sqrt(3))`C. `(-hati+7hatj+5hatk)/(5sqrt(3))`D. `(7hati-7hatj-hatk)/(sqrt(99))`
Consider the line L 1 : x 1 y 2 z 1 312 +++ ==, L2 : x2y2z3 123A. 0 unitB. `17//sqrt(3)` unitsC. `41//sqrt(5)`D. `17//5sqrt(3)` units
If the distance between the plane Ax 2y + z = d and the plane containing the lines2 1x=3 2y=4 3zand3 2x=4 3y=5 4zis 6 , then |d| is
The angle betweenthe lines whose direction cosines satisfy the equations `l+m+n=""0`and `l^2=m^2+n^2`is(1) `pi/3`(2) `pi/4`(3) `pi/6`(4) `pi/2`A. `(pi)/(3)`B. `(pi)/(4)`C. `(pi)/(6)`D. `(pi)/(2)`
The distance of the point `(1,-5,""9)`from the plane `x-y+z=5`measured along the line `x=y=z`is :(1) `3sqrt(10)`(2) `10sqrt(3)`(3) `(10)/(sqrt(3))`(4) `(20)/3`A. `3sqrt(10)`B. `10sqrt(3)`C. `(10)/(sqrt(3))`D. `(20)/(3)`
Equation of the plane containing the straight line `x/2=y/3=z/4` and perpendicular to the plane containing the straight lines `x/2=y/4=z/2` and `x/4=y/2=z/3` isA. `5x+2y-4z=0`B. `x+2y-2z=0`C. `ax+2y-3z=0`D. `x-2y+z=0`
If `L_1` is the line of intersection of the planes `2x-2y+3x-2=0``x-y+z+1=0` and `L_2` is the line of the intersection of the planes `x+2y-z-3=0` `3x-y+2z-1=0`then the distance of the origin from the plane containing the lines `L_1` and `L_2` isA. `(1)/(4sqrt(2))`B. `(1)/(3sqrt(2))`C. `(1)/(2sqrt(2))`D. `(1)/(sqrt(2))`
The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines `r=(hati+hatj)+lambda(hati+2hatj-hatk)" and "r=(hati+hatj)+mu(-hati+hatj-2hatk)` isA. 3B. `(1)/(3)`C. `sqrt(3)`D. `(1)/(sqrt(3))`
Thedistance of the point (1, 0, 2) from the point of intersection of the line `(x-2)/3=(y+1)/4=(z-2)/(12)`and the plane x y + z = 16, is :(1) `2sqrt(14)`(2) 8 (3) `3sqrt(21)`(4) 27A. `2sqrt(14)`B. 8C. `3sqrt(21)`D. 13

Let A be a point on the line `vec(r)=(1-3mu)hati+(mu-1)hatj+(2+5mu)hatk` and `B(3,2,6)` be a point in the space. Then the value of `mu` for which the vector `vec(AB)` is parallel to the plane `x-4y+3z=1` is: (a) `1/8` (b) `1/2` (c) `1/4` (d) `-1/4`A. `(1)/(4)`B. `-(1)/(4)`C. `(1)/(8)`D. `(1)/(2)`

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment