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Find lambda if the vectors veca= hat i...

Find `lambda` if the vectors ` veca= hat i+3\ hat j+ hat k , vecb=2 hat i- hat j- hat k\ and\ vecc=lambda hat i+7\ hatj+3 hat k`are coplanar.

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Three vectors, a, b, c are coplanar if [abc]=0
or or `1(-3+7)-3(6+lambda)+1(14+lambda)=0 `
=`4-18-3lamda+14+lambda`
=`lambda=0`
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NCERT-VECTOR ALGEBRA-SOLVED EXAMPLES
  1. Let vec a= hat i+2 hat jand vecb=2 hat i+ hat j. Is | vec a|=| vec b...

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

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

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

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  5. Find | vec a xx vec b|,if vec a=2 hat i+ hat j+3 hat k and vec b=3 h...

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  6. Find a unit vector perpendicular to each of the vectors ( veca+ vecb)...

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  7. For any two vectors vec a and vec b, we always have |vec a+ vec b|<=|v...

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

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  9. Write all the unit vectors in X Y-p l a n edot

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  10. If hat i+ hat j+ hat k ,2 hat i+5 hat j ,3 hat i+2 hat j-3 hat kand ...

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  11. Find the area of a triangle having the pointsA(1, 1, 1), B(1, 2, 3)and...

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  12. Find the area of a parallelogram whose adjacent sides are given by th...

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  13. Let vec a , vec b and vec cbe three vectors such that | vec a|=3,|...

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  14. Three vectors vec( a), vec(b) and vec(c) satisfy the co...

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  15. Find lambda if the vectors veca= hat i+3\ hat j+ hat k , vecb=2 hat...

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  16. Prove that [ -> a , -> b , -> c+ -> d]=[ -> a , -> b , -> c]+[ -> a , ...

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  17. Show that the vectors -> a= hat i-2\ hat j+3 hat k , -> b=\ 2 hat i...

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  18. Find vec a . ( vec b xx vec c), if vec a=2 hat i+ hat j+3 hat k , ve...

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  19. Prove that [ veca+ vecb , vecb+ vecc , vecc+ veca]=2[ veca , vecb , ve...

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  20. Show that the four points A, B, C and D with position vectors4 hat i+...

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