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The four points whose position vector ar...

The four points whose position vector are `6 hat i - 7 hat j,16 hat i - 29 hat j - 4 hat k, 3 hat i - 6 hat k, 2 hat i + 5 hat j + 10 hat k` are

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$$\text{Consider the four points be }\ A, B, C, D$$ $$ \overrightarrow{\mathrm{OA}}=6 \hat{i}-7 \hat{j}+0 \hat{k} $$ $$ \overrightarrow{\mathrm{OB}}=16 \hat{i}-29_{\mathrm{j}}^{\hat{a}}-4 \hat{k} $$ ...
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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 four points whose position vectors are 6hat i-7hat j,16i-19hat j-4hat k,3hat i-6hat k,2hat i-5hat j+10hat k are coplanar.

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+10hat k are not coplanar.

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.

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 point A , B and C with position vectors vec a =3 hat i - 4 hat j -4 hat k = 2 hat i j + hat k and vec c = hat i - 3 hat j - 5 hat k , respectively from the vertices of a right angled triangle.

Show that the points whose position vectors are (5hat(i) + 6 hat(j) + 7 hat(k)), ( 7 hat(i) - 8hat(j) + 9 hat(k)) and (3 hat(i) + 20 hat(j) + 5 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.

RD SHARMA-SCALAR TRIPLE PRODUCT -Solved Examples And Exercises
  1. Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 ...

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  2. Find lambda so that the vectors vec a=2 hat i- hat j+ hat k ,\ vec b...

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  3. The four points whose position vector are 6 hat i - 7 hat j,16 hat i -...

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  4. For any three vectors a ,\ b ,\ c prove that [ vec a+ vec b\ vec b...

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  5. Show that vectors vec a ,\ vec b ,\ vec c are coplanar if vec a+ v...

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  6. Show that the vectors vec a - vec b, vec b - vec c , vec c - vec a are...

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  7. Evaluate the following: [ hat i\ hat j\ hat k]+[ hat j\ hat k\ ...

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  8. Evaluate : [ hat i hat j hat k]+[ hat j hat k hat i]+[ hat k hat i...

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  9. Find [ vec a\ vec b\ vec c] , when : vec a=2 hat i-3 hat j ,\ vec ...

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  10. Find [ vec a\ vec b\ vec c] , when : vec a= hat i-2 hat j+3 hat k ,...

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  11. Find the volume of the parallelepiped whose coterminous edges are re...

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  12. Find the volume of the parallelepiped whose coterminous edges are r...

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  13. Find the volume of the parallelepiped whose coterminous edges are r...

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  14. Find the volume of the parallelepiped whose coterminous edges are r...

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

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

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

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

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

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

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