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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. **Understanding the Dot Product and Cross Product**: - The dot product of two vectors \( \vec{a} \) and \( \vec{b} \) 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 any two vectors veca and vecb , then |veca.vecb|=|veca xx vecb| when theta is equal to

    A
    0
    B
    `(pi)/(4)`
    C
    `(pi)/(2)`
    D
    `pi`
  • If the angle between the vectors vecA and vecB is theta, the value of the product (vecB xx vecA) * vecA is equal to

    A
    `BA^(2) cos theta`
    B
    `BA^(2) sin theta`
    C
    `BA^(2) sin theta cos theta`
    D
    zero
  • NCERT ENGLISH-VECTOR ALGEBRA-MISCELLANEOUS EXERCISE
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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 veca and vecb be two unit vectors and is the angle between th...

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    12. If -> a , -> b , -> care 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 ixx hat k)+ hat k*...

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    15. यदि veca= vecb + vecc, तब क्या यह सत्य है कि | |veca| = |vecb| +|vecc|...

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

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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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