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For any two vectors -> aand -> bwe alw...

For any two vectors ` -> a`and ` -> b`we always have `| -> adot -> b|lt=| -> a|| -> b|`(Cauchy-Schwartz inequality).

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Knowledge Check

  • For any two sets A and B, B' - A' = ?

    A
    `A cap B`
    B
    `A cup B`
    C
    `A - B`
    D
    `B - A`

  • For any two matrices A and B, we have

    A
    AB=BA
    B
    `AB!=BA`
    C
    AB=O
    D
    None of these

  • For any two matrices A and B , we have

    A
    AB=BA
    B
    `ABneBA`
    C
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    D
    none of these
    • NCERT-VECTOR ALGEBRA-SOLVED EXAMPLES
    1. For any two vectors -> aand -> bwe always have | -> adot -> b|lt=| ...

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    2. If vec a is a unit vector and (vec x - vec a).(vec x + vec a)=8, then ...

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    3. Find | vec a- vec b|,if two vector vec aand vec bare such that | ...

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    4. Find the projection of the veca=2 hat i+3 hat j+2 hat kon the vecb= ha...

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    5. If veca=5 hat i- hat j-3 hat kand vecb= hat i+3 hat j-5 hat kthen sh...

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    6. Find angle thetabetween the vectors veca= hat i+ hat j- hat kand ...

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    7. Find the angle between two vectors vec(a) and vec(b) with magnitude 2 ...

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    8. Show that the points A(2 hat i- hat j+ hat k), B( hat i-3 hat j-5 hat...

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    9. Consider two points P and Q with position vectors vec( O P)=3 vec( a)...

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    10. Find the vector joining the points P(2, 3, 0)and Q( 1, 2, 4)directed...

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    11. Find the unit vector in the direction of the sum of the vectors, vec...

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    12. Write the direction ratios of the vector -&gt; a= hat i+ hat j-2 hat ...

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    13. Represent graphically a displacement of 40 km, 30owest of south.

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    14. Classify the following measures as scalars and vectors.(i) 5 seconds...

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    15. In Figure, which of the vectors are: (i) Collinear (ii) Equal (iii) C...

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    16. Find the values of x, y and z so that the vectors vec a=x hat i+2 hat...

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    17. Let vec a= hat i+2 hat jand vecb=2 hat i+ hat j. Is | vec a|=| vec b...

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    18. Find unit vector in the direction of vector vec a=2 hat i+3 hat j+ ha...

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    19. Find a vector in the direction of vector vec a= hat i-2 hat jthat has...

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    20. If with reference to the right handed system of mutually perpendicula...

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