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If either veca= vec0or vecb= vec0, the...

If either `veca= vec0`or `vecb= vec0`, then ` veca * vecb = 0`But the converse need not be true. Justify your answer with an example.

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To justify the statement that if either \(\vec{a} = \vec{0}\) or \(\vec{b} = \vec{0}\), then \(\vec{a} \cdot \vec{b} = 0\), but the converse need not be true, we can follow these steps: ### Step 1: Understanding the Dot Product The dot product of two vectors \(\vec{a}\) and \(\vec{b}\) is defined as: \[ \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta \] where \(|\vec{a}|\) and \(|\vec{b}|\) are the magnitudes of the vectors, and \(\theta\) is the angle between them. ...
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NCERT ENGLISH-VECTOR ALGEBRA-EXERCISE 10.3
  1. Find the angle between two vectors vec aand vec bwith magnitudes sq...

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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 vec a-5 vec b).(2 vec a+7 vec b)

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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 | -> x|, if for a unit vector -> a ,( -> x- -> a)dot( -> x+ ->...

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  9. Find the magnitude of two vectors vec aand vec b having the same ma...

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  10. If -> adot -> a=0and -> adot -> b=0, then what can be concluded ab...

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  11. If veca , vecb , veccare unit vectors such that veca+ vecb+ vecc= ve...

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  12. If veca=2 hat i+2 hat j+3 hat k , vecb=- hat i+2 hat j+ hat kand vec...

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  13. Show that | vec a| vec b+| vec b| vec a is a perpendicular to | vec a|...

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

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

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

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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 a is a nonzero vector of magnitude a and lambda a nonzero sc...

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