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Vector ` vec c` is perpendicular to vectors ` vec a=(2,-3,1)a n d vec b=(1,-2,3)` and satisfies the condition ` vec x cdot( hat i+2 hat j-7 hat k)=10.` Then vector ` vec c` is equal to a.`(7,5,1)` b. `-7,-5,-1` c. `1,1,-1` d. none of these

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The centre of the circle given by vec r.( hat i+2 hat j+2 hat k)=15a n d| vec r.( hat j+2 hat k)|=4 is a. (0,1,2) b. (1,3,4) c. (-1,3,4) d. none of these

Find a unit vector perpendicular to each of the vector vec a+ vec b and vec a- vec b , where vec a=3 hat i+2 hat j+2 hat k and vec b= hat i+2 hat j-\ 2 hat k

Find a unit vector perpendicular to each of the vectors ( vec a+ vec b) and ( vec a- vec b) , where vec a= hat i+ hat j+ hat k , vec b= hat i+2 hat j+3 hat k .

Find a unit vector perpendicular to both the vector vec(a) = 2 hat(i) + hat(j) - 2 hat(k) and vec(b) = 3 hat (i) - hat (j) + hat (k)

Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i+ hat j- hat kdot Then find [vec a vec b vec c]

Find a unit vector perpendicular to each of the vectors vec(a) + vec(b) and vec (a) - vec(b) where vec(a) = 3 hat (i) + 2 hat (j) + 2 hat (k) and vec(b) = hat (i) + 2 hat (j) - 2 hat (k) .

In each of the following find a unit a vector perpendicular to both vec (a) and vec (b) vec(a) = 2 hat (i) + hat (j) and vec (b) = - hat (i) + hat (k)

For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + hat j - hat k , find the unit vector in the direction of the vector vec a + vec b .

Find a vector magnitude 5 units, and parallel to the resultant of the vectors vec a=2 hat i+3 hat j- hat k and vec b= hat i-2 hat j+ hat kdot

Find the scalar and vector components of vec(a) in the direction of vec(b) where vec(a) = hat (i) + hat(j) and vec(b) = hat (j) + hat (k)

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. The volume of a tetrahedron formed by the coterminous edges vec a ...

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  2. If vec a , vec b , and vec c are three mutually orthogonal unit vector...

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  3. Vector vec c is perpendicular to vectors vec a=(2,-3,1)a n d vec b...

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  4. Given vec a=x hat i+y hat j+2 hat k , vec b= hat i- hat j+ hat k , ve...

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  5. vec aa n d vec b are two unit vectors that are mutually perpendicu...

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  6. If vec ra n d vec s are non-zero constant vectors and the scalar ...

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  7. The scalar vec Adot [( ( vec B+ vec C)xx( vec A+ vec B+ vec C))] eq...

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  8. The volume of he parallelepiped whose sides are given by vec O A=2i...

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  9. For non-zero vectors vec a , vec b ,a n d vec c ,|( vec axx vec b)dot...

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  10. For three vectors vec u , vec va n d vec w which of the following ex...

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  11. Let vec A be a vector parallel to the line of intersection of pla...

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  12. If vec a . vec b=beta and vec axx vec b= vec c ,then vec b is ((beta ...

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  13. Let vec a , vec ba n d vec c be three non-coplanar vecrors and ve...

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  14. Let vec aa n d vec b be mutually perpendicular unit vectors. Then ...

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  15. Value of [ vec axx vec b , vec axx vec c , vec d] is always equal to...

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  16. Let vec aa n d vec b be unit vectors that are perpendicular to each ...

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  17. Let vec r , vec a , vec ba n d vec c be four nonzero vectors such ...

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  18. Let vec a=a1 hat i+a2 hat j+a3 hat k , vec b=b1 hat i+b2 hat j+b3 hat...

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  19. If 4 vec a+5 vec b+9 vec c=0, then ( vec axx vec b)xx[( vec bxx vec c)...

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  20. If vec a , vec b ,a n d vec c are such that [ vec a vec b vec c]=1, v...

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