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A unit vector a makes an angle pi/ 4 wit...

A unit vector a makes an angle `pi/ 4` with z-axis. If `a + i + j` is a unit vector, then a can be equal to

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Vector 1/3(2hati-2hatj+hatk) is (A) a unit vector (B) makes an angle pi//3 with vector (2 hat i-4 hat j+3 hat k) (C) parallel to vector (- hat i+ hat j-1/2 hat k) (D) perpendicular to vector 3 hat i+2 hat j-2 hat k

If veca is unit vector in xy-plane making an angle (pi)/(4) with the x-axis, then veca is equal to -

If a unit vector veca makes angles (pi)/(3) with hati,(pi)/(4) with hatj and an acute angle theta with hatk then find theta and hence , the components of veca .

What is meant by the term unit vector ?

If veca,vecb and vecc are three mutually perpendicular unit vectors and vecd is a unit vector which makes equal angle with veca,vecb and vecc , then find the value of |veca+vecb+vecc+vecd|^(2) .

If veca , vecb , vecc and vecd are four non-coplanar unit vectors such that vecd makes equal angles with all the three vectors veca, vecb, vecc then prove that [vecd vecavecb]=[vecd veccvecb]=[vecd veccveca]

What is the unit vector parallel to vec a=3 hat i+4 hat j-2 hat k ? What vector should be added to vec a so that the resultant is the unit vector hat i ?

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 .

If the incident ray on a surface is along the unit vector vec v , the reflected ray is along the unit vector vec w and the normal is along the unit vector vec a outwards, express vec w in terms of vec a and vec v

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. If the scalar projection of vector x hat i- hat j+ hat k on vector 2...

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  2. If vec a=x hat i+(x-1) hat j+ hat k and vec b=(x+1) hat i+ hat j+a ha...

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  3. A unit vector a makes an angle pi/ 4 with z-axis. If a + i + j is a un...

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  4. if veca, vecb and vecc are there mutually perpendicular unit vectors a...

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  5. If vec a , vec b , and vec c be non-zero vectors such that no two ...

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  6. If vec p , vec q , vec r denote vector vec bxx vec c , vec cxx vec a...

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  7. If vec a and vec b be two non-collinear unit vector such that vec ...

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  8. Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

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  9. Prove that ( vec a.( vec bxx hat i)) hat i+( vec a.( vec bxx hat j)) h...

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  10. For any four vectors, vec a , vec b , vec c and vec d prove that vec...

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  11. If vec a , vec b, and vec c are three vectors such that vec axx ve...

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  12. If vec a= vec p+ vec q , vec pxx vec b=0a n d vec qdot vec b=0, then ...

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  13. If vec a= hat i+ hat j+ hat k and vec b= hat i-2 hat j+ hat k , then ...

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  14. If non-zero vectors veca and vecb are perpendicular to each ot...

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  15. If vec a , vec b , and vec c are mutually perpendicular vectors of ...

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  16. If vec a, vec b, vec c are unit vectors satisfying the condition veca+...

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  17. If three unit vectors vec a , vec b , and vec c satisfy vec a+ vec b...

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  18. If | vec a|+| vec b|=| vec c| and vec a+ vec b= vec c , then find the ...

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  19. Find the angle between the vectors hat i-2 hat j+3 hat k and 3 hat ...

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  20. If vec r. hat i= vec r.hat j= vec r.hat ka n d| vec r|=3, then find t...

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