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Vector vec O A= hat i+2 hat j+2 hat k t...

Vector ` vec O A= hat i+2 hat j+2 hat k` turns through a right angle passing through the positive x-axis on the way. Show that the vector in its new position is `(4 hat i- hat j- hat k)/(sqrt(2))dot`

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The correct Answer is:
`((4)/(sqrt(2)),-(1)/(sqrt(2)),-(1)/(sqrt(2)))`
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Find the vector equation of a plane passing through a point having position vector 2 hat i- hat j+ hat k and perpendicular to the vector 4 hat i+2 hat j-3 hat kdot

The position vectors of the points P and Q are 5 hat i+7 hat j- 2 hat k and -3 hat i+3 hat j+6 hat k respecively. The vector vec A=3 hat i-hat j+hat k passes through the point P and the vector vec B=-3 hat i+2 hat j+4 hat k passes through the point Q. A third vector 2 hat i+7 hat j- 5hat k intersects vectors vec A and vec B . Find the position vectors of the points of intersection

The position vector of the points Pa n dQ are 5 hat i+7 hat j-2 hat k and -3 hat i+3 hat j+6 hat k , respectively. Vector vec A=3 hat i- hat j+ hat k passes through point P and vector vec B=-3 hat i+2 hat j+4 hat k passes through point Q . A third vector 2 hat i+7 hat j-5 hat k intersects vectors Aa n dBdot Find the position vectors of points of intersection.

Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2hat i-hat j+4hat k and is in the direction hat i+2hat j-hat k

The position vectors of the points Pa n dQ with respect to the origin O are vec a= hat i+3 hat j-2 hat k and vec b=3 hat i- hat j-2 hat k , respectively. If M is a point on P Q , such that O M is the bisector of angleP O Q , then vec O M is a. 2( hat i- hat j+ hat k) b. 2 hat i+ hat j-2 hat k c. 2(- hat i+ hat j- hat k) d. 2( hat i+ hat j+ hat k)

MOTION-VECTOR -EXERCISE - 3
  1. The position vectors of the angular points of a tetrahedron are A(3 ha...

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  2. Show that the four points with position vectors4 hat i+8 hat j+12 hat ...

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  3. Examine for coplanarity of the following sets of points 3vec(a) + 2...

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  4. The length of the edge of the regular tetrahedron DABC is 'a'. Point E...

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  5. The position vectors of the four angular points of a tetrahedron ar...

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  6. The position vectors of the four angular points of a tetrahedron ar...

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  7. The position vectors of the four angular points of a tetrahedron ar...

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  8. The position vectors of the four angular points of a tetrahedron ar...

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  9. ABCD is a tetrahedron with pv's of its angular point as A(-5, 22, 5); ...

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  10. Let vec(a) = hat(i) + 2hat(j) + 3hat(k) , vec(b) = 2hat(i) + hat(j) ...

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  11. Let vec(a) = hat(i) + 2hat(j) + 3hat(k) , vec(b) = 2hat(i) + hat(j) ...

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  12. Are the following set of vectors linearly independent? vec(a) = h...

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  13. Are the following set of vectors linearly independent? vec(a) = - 2...

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  14. the resultant of two vectors vec(a) & vec(b) is perpendicular to ve...

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  15. Given three points on the xy plane on O(0, 0), A(1, 0) and B(–1, 0). P...

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  16. Vector vec O A= hat i+2 hat j+2 hat k turns through a right angle ...

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  17. If p vec x +( vec x xx vec a )= vec b ;(p!=0) prove that & vecx...

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  18. Given two orthogonal vectors vec(A) and vec(B) each of length unity ...

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  19. Given two orthogonal vectors vec(A) and vec(B) each of length unity ...

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  20. Which of the following statements is false ?

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