You are given vector `vec(A)=5hat(i)-6.5hat(j)` and `vec(B)=10hat(i)-7hat(j)`. A third vector `vec(C )` lies in the `x-y` plane. Vector `(C )` is perpendicular to vector `vec(A)` and the scalar product of `vec(C )` with `vec(B)` is 15. From this information, find the component of `vec(C )`

You are given vector `vec(A)=5hat(i)-6.5hat(j)` and `vec(B)=10hat(i)-7

1.	You are given vector `vec(A)=5hat(i)-6.5hat(j)` and `vec(B)=10hat(i)-7hat(j)`. A third vector `vec(C )` lies in the `x-y` plane. Vector `(C )` is perpendicular to vector `vec(A)` and the scalar product of `vec(C )` with `vec(B)` is 15. From this information, find the component of `vec(C )`
Answer» Correct Answer - `y=3/4`, `x=39/40` Since `vec(C )` lies in x-y plane, let us assume `vec(C )=xhat(i)+yhat(j)`. Now `vec(C ).vec(A)=orArr5x-6.5y=0`..(i) and `vec(C ).vec(B)=15rArr10x+7y=15`..(ii) From Eqs.(i) and (ii),`y=3/4,x=39/40`

Discussion

No Comment Found

Related InterviewSolutions

When two vectors of magnitudes P and Q are inclined at an angle `theta`, the magnitudes of their resultant is 2P. When the inclination is changed to `180^(@)-theta`, the magnitudes of the resultant is halved. Find the ratio of `P` and `Q`.
If the resultant of two forces of magnitudes `p` and `2p` is perpendicular to `p`, then the angle between the forces isA. `(2pi)/3`B. `(3pi)/4`C. `(4pi)/5`D. `(5pi)/6`
In a methane `(CH_(4)` molecule each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the centre. In coordinates where one of the `C-H` bond in the `hat(i)-hat(j)-hat(k)`, an adjacent `C-H` bond in the `hat(i)-hat(j)-hat(k)` direction. Then angle between these two bonds.A. `cos^(-1)(2/3)`B. `cos^(-1)(2/3)`C. `cos^(-1)(-1/3)`D. `cos^(-1)(1/3)`
If `vecA,vecB,vecC` are mutually perpendicular show that `vecCxx(vecAxxvecB)=0`. Is the converse true?
For the any two vecrtors `vecA` and `vecB`, if `vecA.vecB=|vecAxxvecB|`, the magnitude of `vecC=vecA+vecB` is equal toA. `sqrt(A^(2)+B^(2)`B. `A+B`C. `sqrt(A^(2)+B^(2)+(AB)/(sqrt(2)))`D. `sqrt(A^(2)+B^(2)+sqrt(2)xxAB)`
A magnitude of vector `vecA,vecB` and `vecC` are respectively `12, 5` and `13` units and `vecA+vecB=vecC` then the angle between `vecA` and `vecB` isA. `0`B. `pi`C. `pi//2`D. `pi//4`
A magnitude of vector `vecA,vecB` and `vecC` are respectively `12, 5` and `13` units and `vecA+vecB=vecC` then the angle between `vecA` and `vecB` is
If `vecA = vecB + vecC` and the magnitudes of `vecA, vecB and vecC` are 5,4 and 3 units respecetively, the angle between `vecA` and `vecC` is :A. `cos ^(-1)(3//5)`B. `cos ^(-1)(4//5)`C. `pi//2`D. `sin^(-1)(3//4)`
Two vectors `vec A and vecB` have equal magnitudes.If magnitude of `(vecA+vecB)` is equal to n times ofthe magnitude of `(vecA-vecB)` then the anglebetween `vecA and vecB` is :-A. `cos^(-1) ((n - 1)/(n + 1))`B. `cos^(-1) ((n^(2) - 1)/(n^(2) + 1))`C. `sin^(-1) ((n - 1)/(n + 1))`D. `sin^(-1) ((n^(2) - 1)/(n^(2) + 1))`
Consider three vectors `vecA, vecB and vecC` having magnitudes 4, 5, and 3. These vectors are of similar nature, e.g. these could be there displacement. Apply your answer understanding of vectors algebra to match Column-I with Column-II.

You are given vector `vec(A)=5hat(i)-6.5hat(j)` and `vec(B)=10hat(i)-7hat(j)`. A third vector `vec(C )` lies in the `x-y` plane. Vector `(C )` is perpendicular to vector `vec(A)` and the scalar product of `vec(C )` with `vec(B)` is 15. From this information, find the component of `vec(C )`

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment