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Statement 1: vec a=3 vec i+p vec j+3 ve...

Statement 1: ` vec a=3 vec i+p vec j+3 vec k` and ` vec b=2 vec i+3 vec j+q vec k` are parallel vectors if `p=9//2a n dq=2.` Statement 2: if ` vec a=a_1 vec i+a_2 vec j+a_3 vec ka n d vec b=b_1 vec i+b_2 vec j+b_3 vec k` are parallel, then `(a_1)/(b_1)=(a_2)/(b_2)=(a_3)/(b_3)dot` Which of the following Statements is/are correct ?

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Statement - I: vec(a)=3hat(i)+phat(j)+3hat(k) " and " vec(b)=2hat(i)+3hat(j)+qhat(k) are parallel vectors if p=9/2 " and " q=2 Statement - II: If vec(a)=a_(1)hat(i)+a_(2)hat(j)+a_(3)hat(k) " and " vec(b)=b_(1)hat(i)+b_(2)hat(j)+b_(3)hat(k) are parallel, then a_(1)/b_(1)=a_(2)/b_(2)=a_(3)/b_(3) .

If vec a=2 vec i+3 vec j- vec k , vec b=- vec i+2 vec j-4 vec k a n d vec c= vec i+ vec j+ vec k , then find thevalue of ( vec axx vec b)dot(( vec axx vec c)dot)

Statement 1: | vec a|=3,| vec b|= 4 a n d | vec a+ vec b|=5,t h e n| vec a- vec b|=5. Statement 2: The length of the diagonals of a rectangle is the same.

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

Let vec A=2 vec i+ vec k , vec B= vec i+ vec j+ vec kdot vec C = 4hati-3hatj+7hatk Determine a vector vec R satisfying vec Rxx vec B= vec Cxx vec B and vec R. vec A=0.

Find vec adot vec b when: vec a= hat j- hat k\ a n d\ vec b=2 hat i+3 hat j-2 hat k

if vec a= 5 hat i -hat j -3 hat k and vec b=hat i+3 hat j - 5 hat k , Find vec a . vec b =?

If vec a and vec b are unit vectors such that ( vec a+ vec b).[(2 vec a+3 vec b)xx(3 vec a-2 vec b)]=0 , then angle between veca and vec b is

Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b+ vec c= vec x , vec a dot vec x=1, vec b dot vec x=3/2,| vec x|=2. Then find the angle between vec c and vec x

Statement 1: Lines vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j)a n d vec r=4 hat i- hat k+mu(2 hat i+3 hat k) intersect. Statement 2: vec bxx vec d=0 , then lines vec r= vec a+lambda vec ba n d vec r= vec c+lambda vec d do not intersect.

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. Statement 1:Let A( vec a),B( vec b)a n dC( vec c) be three points such...

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  2. Statement 1: If | vec a+ vec b|=| vec a- vec b|, then vec a and vec b ...

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  3. Statement 1: vec a=3 vec i+p vec j+3 vec k and vec b=2 vec i+3 vec j...

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  4. The position vectors of the vertices A ,Ba n dC of a triangle are th...

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  5. If | vec a|=| vec b|=| vec a+ vec b|=1, then find the value of | vec a...

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  6. Column I, Column II Collinear vectors, p. vec a Coinitial vec...

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  7. Statement 1: | vec a|=3,| vec b|= 4 a n d | vec a+ vec b|=5,t h e n| ...

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  8. A man travelling towards east at 8km/h finds that the wind seems to...

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  9. OABCDE is a regular hexagon of side 2 units in the XY-plane in the ...

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  10. If vec a=7 hat i-4 hat j-4 hat k and vec b=-2 hat i- hat j+2 hat k , ...

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  11. Find a unit vector vec c if vec -i+vec j-vec k bisects the angle betw...

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  12. The vectors 2 hat i+3 hat j ,5 hat i+6 hat j and 8 hat i+lambda hat j ...

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  13. If vec a , vec b and vec c are three non-zero vectors, no two of whic...

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  14. Check whether the given three vectors are coplanar or non-coplanar. -2...

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  15. Prove that the four points 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ...

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  16. Show, by vector methods, that the angularbisectors of a triangle are c...

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  17. Let vec A(t) = f1(t) hat i + f2(t) hat j and vec B(t) = g(t)hat i+g2(...

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  18. Find the least positive integral value of x for which the angle betwee...

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  19. If vectors vec a= hat i+2 hat j- hat k , vec b=2 hat i- hat j+ hat k ...

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  20. Find the values of lambda such that x ,y ,z!=(0,0,0) and ( hat i+ hat ...

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