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If theta is the angle between any two v...

If `theta` is the angle between any two vectors ` veca` and ` vec b`, then `| veca . vecb |=| veca xx vecb|` when `theta` is equal to(A) 0 (B) `pi/4` (C) `pi/2` (D) `pi`

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To solve the problem, we need to find the angle \( \theta \) between two vectors \( \vec{a} \) and \( \vec{b} \) such that the magnitude of their dot product is equal to the magnitude of their cross product. ### Step-by-step Solution: 1. **Write the expressions for dot product and cross product:** - The dot product of two vectors is given by: \[ |\vec{a} \cdot \vec{b}| = |\vec{a}| |\vec{b}| \cos \theta ...
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Knowledge Check

  • If theta is the angle between unit vectors vecA and vecB , then ((1-vecA.vecB))/(1+vecA.vecB)) is equal to

    A
    `tan^(2)(theta//2)`
    B
    `sin^(2)(theta//2)`
    C
    `cot^(2)(theta//2)`
    D
    `cos^(2)(theta//2)`
  • Angle between the vectors sqrt3(veca xx vec b) " and " vec b - (veca .vecb)veca is

    A
    `pi/2`
    B
    0
    C
    `pi/4`
    D
    `pi/3`
  • The angle between the vectors vecA and vecB is theta. The value of vecA(vecAxx vec B) is -

    A
    `A^(2)B`
    B
    zero
    C
    `A^(2)B sin theta`
    D
    `A^(2)B cos theta`
  • NCERT-VECTOR ALGEBRA-MISCELLANEOUS EXERCISE
    1. If theta is the angle between any two vectors veca and vec b, then...

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    2. The two adjacent sides of a parallelogram are 2 hat i-4 hat j+5 hat k...

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    3. Show that the direction cosines of a vector equally inclined to the a...

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    4. Write down a unit vector in XY-plane, making an angle of 30° with the...

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    5. A girl walks 4 km towards west, then she walks 3 km in a direction 30...

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    6. Find the scalar components and magnitude of the vector joining the po...

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    7. Find the value of x for which x( hat i+ hat j+ hat k)is a unit vector...

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    8. Let vec a= hat i+4 hat j+2 hat k , vec b=3 hat i-2 hat j+7 hat kand ...

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    9. The scalar product of the vector hat i+ hat j+ hat kwith a unit vect...

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    10. If theta is the angle between two vectors veca and vecb, then veca...

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    11. Let -> aand -> bbe two unit vectors and is the angle between them...

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    12. If veca , vecb , veccare mutually perpendicular vectors of equal ma...

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    13. Prove that (veca+ vecb)*( veca+ vecb)=|veca|^2+| vecb|^2, if and only ...

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    14. The value of hat i . ( hat jxx hat k)+ hat j . ( hat i times hat k)+...

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    15. State True or False: If vec a= vecb + vec c then |veca |= |vec b| ...

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

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    17. If veca= hat i+ hat j+ hat k, vecb=2 hat i- hat j+3 hat k and vecc...

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    18. Find a vector of magnitude 5 units, and parallel to the resultant of ...

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    19. Show that the points A(1,2,8) , B(5,0,2) and C(11,3,7)are collinear, ...

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