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Show that four points whose position vectors are `6 hat i-7 hat j ,\ 16 i-19 hat j-4 hat k ,\ 3 hat i-6 hat k ,\ 2 hat i-5 hat j+10\ hat k` are coplanar.

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$$\text{Suppose the four points be} A, B, C, D ,$$ $$ \overrightarrow{\mathrm{OA}}=6 \hat{1}-7 \hat{j}+0 \hat{\mathrm{k}} $$ $$ \overrightarrow{O B}=16 \hat{1}-29 \hat{j}-4 \hat{k} $$ ...
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The four points whose position vector are 6hat i-7hat j,16hat i-29hat j-4hat k,3hat i-6hat k,2hat i+5hat j+10k are

Show that the four points having position vectors 6hat i-7hat j,16hat i-19hat j-4hat k,3hat j-6hat k,2hat i-5hat j+10k are coplanar.

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Show that the points having position vectors 6hat i-7hat j,16hat i-19hat j-4hat k,3hat j-6hat k,2hat i+5hat j+10hat k are not coplanar.

Show that the points whose position vectors are 5 hat i+5 hat k ,\ 2 hat i+ hat j+3 hat k\ a n d-4 hat i+3 hat j- hat k are collinear.

Show that the points whose position vectors are 5hat i+5hat k,2hat i+hat j+3hat k and -4hat i+3hat j-hat k are collinear

Find the value of lambda for which the four points with position vectors -hat j-hat k,4hat i+5hat j+lambdahat k,3hat i+9hat j+4hat k and 4hat i+4hat j+4hat k are coplanar.

Find the value of lambda for which the four points with position vectors hat j-hat k,4hat i+5hat j+lambdahat k,3hat i+9hat j+4hat k and -4hat i+4hat j+4hat k are coplanar.

Prove that the four points having position vectors are coplanar: 2hat i-hat j+hat k,hat i-3hat j-5hat k and 3hat i-4hat j-4hat k

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RD SHARMA-SCALAR TRIPLE PRODUCT -Solved Examples And Exercises
  1. Show that each of the following triads of vectors are coplanar: vec...

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  2. Show that each of the following triads of vectors are coplanar: vec...

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  3. Show that each of the following triads of vectors are coplanar: ve...

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  4. Find the value of lambda so that the following vectorts are coplana...

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  5. Find the value of lambda so that the following vectorts are coplana...

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  6. Find the value of lambda so that the following vectorts are coplana...

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  7. Find the value of lambda so that the following vectorts are coplanar...

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  8. Show that the points having position vectors 6 hat i-7 hat j ,\ 16 ...

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  9. Show that the points A(-1,\ 4,\ -3),\ B(3,\ 2,\ -5),\ C(-3,\ 8,\ -5)a ...

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  10. Show that four points whose position vectors are 6 hat i-7 hat j ,\...

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  11. Find the value of lambda for which the four points with position ve...

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  12. Prove that ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)}=0

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  13. Let vec a=hat i+hat j+hat k and vec b=i and vec c=c1 hat i + hat c2...

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  14. Find lambda for which the points A(3,\ 2,\ 1),\ B(4,\ lambda,\ 5),\ C(...

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  15. Write the value of [2 hat i\ 3 hat j\ 4 hat k]

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  16. Write the value of [ hat i+ hat j\ hat j+ hat k\ hat k+ hat i]

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  17. Write the value of [ hat i- hat j\ hat j- hat k\ hat k- hat i]

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  18. Find the values of a for which are vectors vecalpha= hat i+2 hat j...

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  19. Find vec a.( vec bxx vec c)\ if\ vec a=2 hat i+ hat j+3 hat k ,\ ve...

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  20. If the vectors 4 hat i+11 hat j+m hat k ,\ 7 hat i+2 hat j+6 hat k\ a ...

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