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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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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))`
  • NCERT-VECTOR ALGEBRA-EXERCISE 10.3
    1. Find the angle between two vectors vecaand vecbwith magnitudes sqrt...

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    2. Find the projection of the vector hat i- hat jon the vector hat i+ ...

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    3. Find the angle between the vectors hat i-2 hat j+3kand 3 hat i-2 hat...

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    4. Show that each of the given three vectors is a unit vector: 1/7(2 hat...

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    5. Find the projection of the vector hat i+3 hat j+7 hat kon the vector...

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    6. Evaluate the product (3 veca-5 vecb)cdot(2 veca+7 vecb)

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    7. Find | vec a|and | vec b|, if ( vec a+ vec b)dot(( vec a- vec b))=8a...

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    8. Find | vecx|, if for a unit vector veca ,( vec x- veca) .( vecx+ ve...

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    9. Find the magnitude of two vectors vec aand vecbhaving the same magn...

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    10. If veca cdot veca=0and veca cdot vecb=0, then what can be conclude...

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    11. If veca , vec b , vec c are unit vectors such that veca+ vec b+ vec...

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    12. If veca=2 hat i+2 hat j+3 hat k , vecb=- hat i+2 hat j+ hat k and v...

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    13. Show that | veca| vecb+| vecb| veca is perpendicular to | vec a| vec ...

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    14. Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10 , 1)are colli...

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    15. Show that the vectors 2 hat i- hat j+ hat k , hat i-3 hat j-5 hat kan...

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    16. If either veca= vec0or vecb= vec0, then veca * vecb = 0 But the con...

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    17. If the vertices A, B, C of a triangle ABC are (1, 2, 3), (1, 0, 0), (...

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    18. If vec ais a nonzero vector of magnitude a and lambdaa nonzero scal...

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