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Show that the vector hat i+ hat j+ hat...

Show that the vector ` hat i+ hat j+ hat k`is equally inclined to the axes OX, OY and OZ.

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The correct Answer is:
`therefore vec r` is equally inclined to the axes.
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The units vectors orthogonal to the vector - hat i + 2hat j + 2hat k and making equal angles with the X and Y axes islare) :

Vector vec a in the plane of vec b=2 hat i+ hat ja n d vec c= hat i- hat j+ hat k is such that it is equally inclined to vec ba n d vec d where vec d= hat j+2 hat kdot The value of vec a is a. ( hat i+ hat j+ hat k)/(sqrt(2)) b. ( hat i- hat j+ hat k)/(sqrt(3)) c. (2 hat i+ hat j)/(sqrt(5)) d. (2 hat i+ hat j)/(sqrt(5))

Show that the vectors 2 hat i - hat j + hat k , hat i - 3 hat j - 5hat k and 3hat i - 4 hat j - 4 hat k from the vertices of a right angled triangle.

Show that the line of intersection of the planes vec rdot( hat i+2 hat j+3 hat k)=0a n d vec r=(3 hat i+2 hat j+ hat k)=0 is equally inclined to ia n dkdot Also find the angle it makes with jdot

The unit vector orthogonal to vector hat i+ hat j+2 hat k and making equal angles with the x and y-axis a. +-1/3(2 hat i+2 hat j- hat k) b. +-1/3( hat i+ hat j- hat k) c. +-1/3(2 hat i-2 hat j- hat k) d. none of these

Show that the vectors 2 hat i - 3 hat j + hat k , - 4hati - hat j + 3 hat k and -2 hat i - 4hatj + 4 hat k are coplanar.

Show that the vectors 2 hat i + 3 hat j + 4 hat k and 4 hat i + 6 hat j + 8 hat k are collinear.

The projection of the vector hat i + hat j + hat k along the vector hat j is

Prove that the vectors 3 hat i + hat j + 3 hat k and hat i - hat k are perpendicular.

Thescalar product of the vector hat i + hat j + hat k with a unit vector along the sum of vectors 2 hat i + 4 hat j - 5 hat k and lambda hat i + 2 hat j + 3 hat k is equal to one. Find the value of lambda .

NEW JOYTHI PUBLICATION-VECTOR ALGEBRA-SOLUTIONS TO NCERT TEXT BOOK EXERCISE 10.2
  1. Compute the magnitude of the following vectors. veca = hat i + hat j...

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  2. Write two different vectors having the same magnitude.

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  3. Write two different vectors having the same direction.

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  4. Find the values of x and y so that the vectors 4 hat i + 5 hat j and ...

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  5. Find the scalar and vector components of the vector with initial point...

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  6. Find the sum of the vectors veca = hat i - 2 hat j + hat k, vec b = - ...

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  7. Find the unit vector in the direction of the vector vec a = hat i - ha...

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  8. Find the unit vector in the direction of vector vec(PQ), where P and Q...

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  9. For given vectors vec a = 2 hat i - hat j + 2 hat k and vec b = - hat ...

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  10. Find a vector in the direction of vector 5 hat i - hat j + 2 hat k whi...

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  11. Show that the vectors 2 hat i-3 hat j+4 hat kand -4 hat i+6 hat j-8 h...

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  12. Find the direction cosines of the vector hat i + 2 hat j + 2 hat k.

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  13. Find the direction cosines of the vector joining the points A(-1, 2, 3...

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  14. Show that the vector hat i+ hat j+ hat kis equally inclined to the a...

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  15. Find the position vector of a point R which divides the line joining t...

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  16. Find the position vector of the midpoint of the vector joining the poi...

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  17. Show that the points A, B and C with position vectors vec a = 3 hat i ...

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  18. In triangle ABC, which of the following is not true?

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  19. If vec a and vec b are collinear vectors, then which of the following ...

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