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Find the volume of the parallelepiped whose coterminous edges are represented by the vector: ` vec a=11 hat i ,\ vec b=2 hat j ,\ vec c=13 hat k` .

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To find the volume of the parallelepiped whose coterminous edges are represented by the vectors \( \vec{a} = 11 \hat{i} \), \( \vec{b} = 2 \hat{j} \), and \( \vec{c} = 13 \hat{k} \), we will use the formula for the volume \( V \) given by the scalar triple product: \[ V = |\vec{a} \cdot (\vec{b} \times \vec{c})| \] ### Step 1: Calculate the cross product \( \vec{b} \times \vec{c} \) ...
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Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=hat i+hat j+hat k,vec b=hat i-hat j+hat k,vec c=hat i+2hat j-hat k

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors: vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+2 hat j- hat k , vec c=3 hat i- hat j+2 hat k vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+2 hat j- hat k , vec c=3 hat i- hat j-2 hat k vec a=11 hat i , vec b=2 hat j- hat k , vec c=13 hat k vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j- hat k

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=2hat i+3hat j+4hat k,vec b=hat i+hat i+2hat j-hat k,vec c=3hat i-hat j+2hat k

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=2hat i-3hat j+4hat k,vec b=hat i+hat i+2hat j-hat k,vec c=3hat i-hat j-2hat k

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors vec(a)=2hat(i)-3hat(j)+hat(k),vec(b)=hat(i)-hat(j)+2hat(k) and vec(c)=2hat(i)+hat(j)-hat(k) .

Find the volume of the parallelepiped whose edges are represented by the vectors vec(a)=(2hat(i)-3hat(j)+4hat(k)), vec(b)=(hat(i)+2hat(j)-hat(k)) and vec(c)=(3hat(i)-hat(j)+2hat(k)) .

Find the altitude of a parallelepiped whose three coterminous edtges are vectors vec A= hat i+ hat j+ hat k , vec B=2 hat i+4 hat j- hat ka n d vec C= hat i+ hat j+3 hat kw i t h vec Aa n d vec B as the sides of the base of the parallepiped.

Find the area of the parallelogram whose adjacent sides are represented by the vectors (i) vec(a)=hat(i) + 2 hat(j)+ 3 hat(k) and vec(b)=-3 hat(i)- 2 hat(j) + hat(k) (ii) vec(a)=(3 hat(i)+hat(j) + 4 hat(k)) and vec(b)= ( hat(i)- hat(j) + hat(k)) (iii) vec(a) = 2 hat(i)+ hat(j) +3 hat(k) and vec(b)= hat(i)-hat(j) (iv) vec(b)= 2 hat(i) and vec(b) = 3 hat(j).

Find the area of the parallelogram whose diagonals are represented by the vectors vec(d)_(1)=(2 hat(i) - hat(j)+ hat(k)) and vec(d)_(2) = (3 hat(i) + 4 hat(j) - hat(k)).

RD SHARMA-SCALAR TRIPLE PRODUCT -Solved Examples And Exercises
  1. Find the volume of the parallelepiped whose coterminous edges are re...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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