Let `vecu,vecv,vecw` be such that `|vecu|=1,|vecv|=2,|vecw|3`. If the projection of `vecv along vecu` is equal to that of `vecw along vecv,vecw` are p

Monjur Alahi

Let `vecu,vecv,vecw` be such that `|vecu|=1,|vecv|=2,|vecw|3`. If the projection of `vecv along vecu` is equal to that of `vecw along vecv,vecw` are perpendicular to each other then `|vecu-vecv+vecw|` equals (A) 2 (B) `sqrt(7)` (C) `sqrt(14)` (D) `14`
A. 2
B. `sqrt7`
C. `sqrt14`
D. 14


0 like 0 dislike
1 views
Share with your friends

1 Answers

Salim Ahmed Kawsar

Call

Correct Answer - c
Given `vecv.vecu = vecw .vecu`
`and vecv bot vecw Rightarrow vecv .vecw = 0`
Now, `|vecu - vecu + vecw|^(2)`
` |vecu|^(2) + |vecv|^(2) + |vecw|^(2) = 2vecu.vecv`
` - 2vecw. Vecu + 2vecu .vecw`
1 + 4+ 9
`so |vecu -vecv - vecw|= sqrt14`

0 like 0 dislike
1 views
Talk Doctor Online in Bissoy App
Let `L_(1)` be the line `vecr_(1)=2hati+hatj-hatk+lamda(hati+2hatk)` and let `L_(2)` be the line `vecr_(2)=3hati+hatj-hatk+mu(hati+hatj+hatk)`. Let `p

Correct Answer - a Equation of the plane containing `L_(1),A(x-2)+B(y-1)+C(z+1)=0` where `A+2C=0,A+B-C=0` `impliesA=-2C-,B=3C,C=C` `implies"Plane is"-2(x-2)+3(y-1)+z+1=0` or `2x-3y-z-2=0` Hence, `p=|(-2)/(sqrt14)|=sqrt((2)/(7))`

2 Answers 1 views
A projectile is projected from ground with initial velocity `vecu=u_(0)hati+v_(0)hatj`. If acceleration due to gragvity (g) is along the negative y-di

Correct Answer - B Horizontal range `R=(2u_(x)u_(y))/(g)=(2u_(0)v_(0))/(g)`

2 Answers 1 views
Let `A-=(3,-4),B-=(1,2)`. Let `P-=(2k-1+1)` be a variable point such that `PA+PB` is the minimum. Then k is

Correct Answer - C We know that `PA+PBgeAB` (by triangle inequality). So, `PA+PB` is the minimum if `PA+PB=AB` , i.e., A,P,B are collinear. Therefore, `|{:(3,,-4,,1),(1,,2,,1),(2k-1,,2k+1,,1):}|=0` or `3(2-2k-1)+4(1-2k+1)+1(2k+1)+1(2k+1-4k+2)=0` or `3-6k+8-8k+3-2k=0` or `14-16k=0`...

2 Answers 1 views
If `vecu,vecv and vecw` are three non coplanar vectors then `(vecu+vecv-vecw).(vecu-vecc)xx(vecv-vecw)` equals (A) `vecu.vecvxxvecw` (B) `vecu.vecwxxv

`(vecu+vecv-vecw).(vecu-vecv)xx(vecv-vecw)=)(vecu+vecv-vecw).(vecuxxvecv-vecuxxvecw-vecvxxvecv+vecvxxvecw)` `=(vecu+vecv-vecw).(vecuxxvecv-vecuxxvecw+vecvxxvecw)` `= 0-0+vecu.(vecvxxvecw)+0-vecv.(vecuxxvecw)+0-vecw.(vecuxxvecv)+0-0` `[vecu vecv vecw]+[vecv vecw vecu] - [vecwvecuvecv]=vecu.(vecvxxvecw)`

2 Answers 1 views
Let `vecu=hai+hatj,vecv=hati-hatj and vecw=hati+2hatj+3hatk`. If `hatn` isa unit vector such that `vecu.hatn=0 and vecv.hatn=0, |vecw.hatn|` is equal

`hatn=a_(1)hati=a_(2)hatj+a_(3)hatk " where " a_(1)^(2)+a_(2)^(2)+a_(3)^(2)=1` Given that `vecu.hatn=0 Rightarrowa_(1)+a_(2)=0` `Also, vecv.hatn=0 Rightarrowa_(1)-a_(2)=0` `a_(1)=a_(2)=0` `a_(3)=1or-1` `hatn=hatk or-hatk` `|vecwhatn|=3`

2 Answers 1 views
Let `vecV=2hati+hatj-hatk` and `vecW=hati+3hatk`. It `vecU` is a unit vector, then the maximum value of the scalar triple product `[(vecU, vecV, vecW)

Correct Answer - c Given that `vecV = 2hati +hatj -hatk and vecW =hati + 3hatk and vecU` is a unit vector ` |vecU|=1` Now `|vecU vecV vecW] = vecU.(vecV xx...

2 Answers 1 views
For three vectors `vecu,vecv,vecw` which of the following expressions is not eqal to any of the remaining three?

Correct Answer - c `[ vecu vecv vecw] = [vecv vecw vecu] = [vecw vecu vecv]` but `[vecv vecu vecw]=- [vecu vecv vecw]`

2 Answers 1 views
Let `A B C` be a triangle such that `/_A C B=pi/6` and let `a , ba n dc` denote the lengths of the side opposite to `A , B ,a n dC` respectively. The

Correct Answer - B Using cosine rule for `angleC`, we get `(sqrt3)/(2) = ((x^(2) + x+1)^(2) + (x^(2) -1)^(2) - (2x + 1)^(2))/(2 (x^(2) + x + 1) (x^(2) -1))` or...

2 Answers 1 views
Let `f(x)=x^(3)+x+1`, let `p(x)` be a cubic polynomial such that the roots of `p(x)=0` are the squares of the roots of `f(x)=0` , then

Correct Answer - A::B::C::D `(a,b,c,d)` Let `x=alpha^(2)`, `alpha=sqrt(x)`, put this value in `x^(3)+x+1=0` We get `xsqrt(x)+sqrt(x)+1=0` `sqrt(x)(x+1)=-1` `impliesx(x+1)^(2)=1` `impliesx^(3)+2x^(2)+x-1=0` `impliesp(x)=x^(3)+2x^(2)+x-1` `impliesp(1)=3` Also `p(1)` is odd when `n` is odd or even.

2 Answers 1 views
A ball is projected from ground in such a way that after 10 seconds of projection it lands on ground 500 m away from the point of projection. Find out

Correct Answer - (i)`theta=45^(@)` (ii)`50sqrt(2)m//s` (iii)`50m//sec`

2 Answers 10 views
X