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Show that the points A,B,C with position...

Show that the points A,B,C with position vectors `(3hat(i)- 2 hat(j)+ 4hat(k)),(hat(i) + hat(j) +hat(k))` and `(-hat(i)+ 4 hat(j)- 2 hat(k))` respectively are collinear.

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Show that the four points A, B, C and D with position vectors 4hat(i)+5hat(j)+hat(k), -(hat(j)+hat(k)),3hat(i)+9hat(j)+4hat(k) and 4(-hat(i)+hat(j)+hat(k)) respectively are coplanar.

show that the points whose position vectors are (-2hat(i) +3hat(j) +5hat(k)) (hat(i)+2hat(j)+3hat(k)) " and " (7hat(i) -hat(k)) are collinear.

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Show that the four points A,B,C and D with position vectors 4hat i+5hat j+hat k,-(hat j+hat k),3hat j+9hat j+4hat k and 4(-hat i+hat j+hat k) respectively are 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.

The position vectors of three points A,B anc C (-4hat(i) +2hat(j) -3hat(k)) (hat(i) +3hat(j) -2hat(k)) "and " (-9hat(i) +hat(j) -4hat(k)) respectively . Show that the points A,B and C are collinear.

Show that the points A,B,C with position vectors 2hat i-hat j+hat k,hat i-3hat j-5hat k and 3hat i-4hat j-4hat k respectively,are the vertices of a right angled triangle.Also,find the remaining angles of the triangle.

Show that the vectors hat(i)-3hat(j)+4hat(k),2hat(i)-hat(j)+2hat(k)and 4hat(i)-7hat(j)+10hat(k) are coplanar.

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RS AGGARWAL-CROSS,OR VECTOR, PRODUCT OF VECTORS-Exercise 24
  1. Find a vector of magnitude 6 which is perpendicular to both the vector...

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  2. Find a unit vector perpendicular to each of the vectors ( -> a+ -> ...

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  3. Find the angle between two vectors vec(a) and vec(b) with magnitudes 1...

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  4. Let vec a= hat i- hat j ,\ vec b=3 hat j- hat k and vec c=7 hat i- h...

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  5. If vec(a)=(4hat(i)+ 5 hat(j) - hat(k)),vec(b)=(hat(i)-4 hat(j)+ 5 hat(...

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  6. Prove that |vec(a) xx vec(b)|=(vec(a)*vec(b)) tan theta," where " the...

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  7. Write the value of p for which vec a=3 hat i+2 hat j+9 hat k\ a n d\ ...

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  8. verify thatvec(a) xx (vec(b)+ vec(c))=(vec(a) xx vec(b))+(vec(a) xx ve...

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  9. Find the area of the parallelogram whose adjacent sides are represente...

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  10. Find the area of the parallelogram whose diagonals are represented by...

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  11. Find the area of the trinagle whose two adjacent sides are determined ...

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  12. Using vectors, find the area of Delta ABC whose vertices are (i) A...

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  13. Using vector method, show that the given points A,B,C are collinear: ...

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  14. Show that the points A,B,C with position vectors (3hat(i)- 2 hat(j)+ 4...

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  15. Show that the points having position vectors vec(a), vec(b),(vec(c)=3 ...

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  16. Show that the points having position vectors (-2vec(a) + 3 vec(b)+5vec...

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  17. Find a unit vector perpendicular to the plane ABC, where the coordi...

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  18. If vec(a)= ( hat(i)- 2hat(j) + 3hat(k)) and vec(b)=(hat(i)-3hat(k)) ...

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  19. If | vec a|=2,|b|=5 and | vec ax vec b|=8, find vec adot vec bdot

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  20. If |vec(a)| = 2, |vec(b)|= 7 and (vec(a) xx vec(b))=(3 hat(i) + 2 hat(...

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