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Determine alpha such that a vector vec ...

Determine `alpha` such that a vector ` vec r` is at right angles to each of the vectors ` vec a=alpha hat i+ hat j+3 hat k , vec b=2 hat i+ hat j-alpha hat k , vec c=-2 hat i+alpha hat j+3 hat k`

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Determine lambda such that a vector vec(r) is at right angles to each of the vectors vec(a) = lambda hat(i) + hat(j) + 3hat(k), vec(b) = 2hat(i) + hat(j) - lambda hat(k), vec(c) = -2hat(i) + lambda hat(j) + 3hat(k) .

Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 hat i+4 hat j-2 hat k\ a n d\ vec c=4 hat i-2 hat j-2 hat k are coplanar.

Find the angle between the vectors vec a= hat i+hat j-hat k and vec b=hat i-hat j+hat k

Find lambda so that the vectors vec a=2 hat i- hat j+ hat k ,\ vec b= hat i+2 hat j-3 hat k\ a n d\ vec c=3 hat i+lambda hat j+5 hat k are coplanar.

Find | vec a xx vec b|, if vec a=2 hat i+ hat j+3 hat k and vec b=3 hat i+5 hat j-2 hat k .

Find the projection of the vector vec a=2 hat i+3 hat j+2 hat k on the vector vec b=2 hat i+2 hat j+ hat k .

Show that the vectors vec a=3 hat i-2 hat j+ hat k , vec b= hat i+3 hat j+5 hat k , vec c=2 hat i+ hat j-4 hat k form a right angled triangle.

Show that the vectors vec a=3 hat i-2 hat j+ hat k ,\ vec b= hat i-3 hat j+5 hat k ,\ vec c=2 hat i+ hat j-4 hat k form a right angled triangle.

Show that each of the following triads of vectors are coplanar: vec a= hat i-2 hat j+3 hat k ,\ vec b=-2 hat i+3 hat j-4 hat k ,\ vec c= hat i-3 hat j+5 hat kdot

Find vec a.( vec bxx vec c)\ if\ vec a=2 hat i+ hat j+3 hat k ,\ vec b=- hat i+2 hat j+ hat k\ a n d\ vec c=3 hat i+ hat j+2 hat kdot

RD SHARMA ENGLISH-SCALAR TRIPLE PRODUCT -All Questions
  1. Simplify: [ vec a- vec b vec b- vec c vec c- vec a]

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  2. If the vectors vecalpha=a hat i+a hat j+c hat k , vecbeta= hat i+ hat...

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  3. Determine alpha such that a vector vec r is at right angles to each o...

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  4. Find the range of f(x)=sin^(-1)x+tan^(-1)x+cos^(-1)xdot

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  5. If vec a , vec b , vec c are three non-coplanar vectors, prove that [...

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  6. For any three vectors a b,c, show that vec a xx (vec b +vec c)+vec b x...

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  7. Let vec a , vec b , vec c be three non-zero vectors such that vec c ...

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  8. Let vec a , vec ba n d vec c , be non-zero non-coplanar vectors. Prov...

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  9. Find the altitude of a parallelepiped determined by the vectors ve...

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  10. Let vec a , vec b , vec c , be three non-zero vectors. If vec a .(ve...

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  11. If the vectors vecalpha=a hat i+ hat j+ hat k , vecbeta= hat i+b hat ...

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  12. If a is a non-zero real number, then prove that the vectors vecalph...

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  13. If vec a+vec b+vec c=0, prove that (vec a xx vec b)=(vec b xx vec c)=(...

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  14. Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 ...

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  15. Find lambda so that the vectors vec a=2 hat i- hat j+ hat k ,\ vec b...

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  16. The four points whose position vector are 6 hat i - 7 hat j,16 hat i -...

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  17. For any three vectors a ,\ b ,\ c prove that [ vec a+ vec b\ vec b...

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  18. Show that vectors vec a ,\ vec b ,\ vec c are coplanar if vec a+ v...

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  19. Show that the vectors vec a - vec b, vec b - vec c , vec c - vec a are...

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  20. What can you conclude about four non zero vectors vec a ,\ vec b ...

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