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Show that the vectors 2hat(i)-hat(j)+hat...

Show that the vectors `2hat(i)-hat(j)+hat(k),3hat(i)-4hat(j)-4hat(k), hat(i)-3hat(j)-5hat(k)` form a right angled triangle.

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show that the vectors 3 hat(i)- 2hat(j)+ hat(k), hat(i)-3hat(j)+5hat(k) and 2hat(i)+ hat(j)- 4 hat(k) form a right angled triangle

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

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

Show that the points A, B, C with position vector 2hat(i)-hat(j)+hat(k),hat(i)-3hat(j)-5hat(k)and3hat(i)-4hat(j)+4hat(k) respectively are the vector of a right angled triangle. Also, find the remaining angles of the triangle.

Determine whether the three vectors 2hat(i)+3hat(j)+hat(k),hat(i)-2hat(j)+2hat(k)and3hat(i)+hat(j)+3hat(k) are coplanar.

Show that the points whose position vectors are 2hat(i) + 3hat(j) - 5hat(k), 3hat(i) + hat(j) - 2hat(k) and 6hat(i) - 5hat(j) + 7hat(k) are collinear.

Show that the vectors 2 hat i - hat j + hat k , hat i - 3 hat j - 5hat k and 3hat i - 4 hat j - 4 hat k from the vertices of a right angled triangle.

Show that the lines vec(r)=(6hat(i)+hat(j)+2hat(k))+s(hat(i)+2hat(j)-3hat(k)),andvec(r)=(3hat(i)+2hat(j)-2hat(k))+t(2hat(i)+4hat(j)-5hat(k)) are skew lines and hence find the shortest distance between them.

Show that four points whose position vectors are given 6hat(i)-7hat(j) ; 16hat(i)-19hat(i)-4hat(k) ; 3hat(i)-6hat(k) ; 2hat(i)-5hat(j)+10hat(k) are co-planar

SURA PUBLICATION-VECTOR ALGEBRA -I-EXERCISE 8.2
  1. Find the direction cosines and direction ratios for the following vect...

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  2. Find the direction cosines and direction ratios for the following vect...

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  3. Find the direction cosines and direction ratios for the following vect...

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  4. Find the direction cosines and direction ratios for the following vect...

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  5. A triangle is formed by joining the points (1,0,0), (0,1,0) and (0,0,1...

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  6. If (1)/(2),(1)/(sqrt(2)) a are the direction cosines of some vector, t...

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  7. If (a,a+b,a+b+c) is one set of direction ratios of the line joining (1...

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  8. Show that the vectors 2hat(i)-hat(j)+hat(k),3hat(i)-4hat(j)-4hat(k), h...

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  9. Find the value of lambda for which the vectors veca=3hat(i)+2hat(j)+9h...

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

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  11. Show that the vectors are coplanar 2hat(i)+3hat(j)+hat(k),hat(i)-hat...

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  12. Show that the points whose position vectors 4hat(i)+5hatj+hatk,-hatj-h...

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  13. If veca=2hati+3hatj-4hatk,vecb=3hati-4hatj-5hatk, and vecc=-3hati+2hat...

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  14. If veca=2hati+3hatj-4hatk,vecb=3hati-4hatj-5hatk, and vecc=-3hati+2hat...

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  15. The position vectors of the vertices of a triangle are hati+2hatj+3hat...

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  16. Find the unit vector parallel to 3veca-2vecb+4vecc,"if"" "veca=3hati-h...

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  17. The position vectors veca,vecb,veccof three points satisfy the relatio...

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  18. The position vectors of the points P,Q,R,S are hati+hatj+hatk,2hati+5h...

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  19. Find the value or values of m for which m (hati+hatj+hatk) is a unit v...

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  20. Show that the points A (1,1,1), B (1,2,3) and C (2,-1,1) are vertices ...

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