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Find the angle between two vectors vec...

Find the angle between two vectors ` veca`and ` vecb`with magnitudes `sqrt(3)`and 2 respectively having ` veca cdot vecb=sqrt(6)`

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AI Generated Solution

To find the angle between two vectors \( \vec{a} \) and \( \vec{b} \) with given magnitudes and dot product, we can use the formula for the dot product of two vectors: \[ \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta \] ### Step 1: Identify the given values - Magnitude of \( \vec{a} \): \( |\vec{a}| = \sqrt{3} \) ...
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Knowledge Check

  • The angle between two vectors veca and vecb with magnitudes sqrt(3) and 4, respectively and veca.vecb = 2sqrt(3) is:

    A
    `pi/6`
    B
    `pi/3`
    C
    `pi/2`
    D
    `(5pi)/2`
  • The angle between two vectros vecaandvecb with magnitudes sqrt3 and 4, respectively and veca.vecb=2sqrt3 is

    A
    `(pi)/(6)`
    B
    `(pi)/(3)`
    C
    `(pi)/(2)`
    D
    `(5pi)/(2)`
  • If the angles between the vectors veca and vecb,vecb and vecc,vecc an veca are respectively pi/6,pi/4 and pi/3 , then the angle the vector veca makes with the plane containing vecb and vecc , is

    A
    `cos^(-1)sqrt(1-sqrt(2//3))`
    B
    `cos^(-1)sqrt(2-sqrt(3//2))`
    C
    `cos^(-1)sqrt(sqrt(3//2)-1)`
    D
    `cos^(-1)sqrt(sqrt(2//3))`
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