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Show that the vectors -hati-2hatj-6hatk,...

Show that the vectors `-hati-2hatj-6hatk,2hati-hatj+hatk" "`and `-hati+3hatj+5hatk,` form a right angled triangle.

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Show that the vectors 3hati-2hatj+hatk,hati-3hatj+5hatk and 2hati+hatj-4hatk form a right angled triangle.

Show that the vectors 2hati-hatj+hatk,hati-3hatj-5hatkand3hati-4hatk form the vertices of a right angled triangle.

Show that the vectors hati+2hatj-3hatk , 2hati-hatj+2hatk and 3hati+hatj-hatk are coplanar.

Prove that the points whose position vectors 2hati+4hatj+3hatk,4hati+hatj+9hatk and 10hati-hatj+6hatk form a right angled triangle.

Show that the points whose positions vectors 4hati-3hatj+hatk,2hati-4hatj+5hatk,hati-hatj from a right angled triangle.

Prove that points hati+2hatj-3hatk, 2hati-hatj+hatk and 2hati+5hatj-hatk form a triangle in space.

Show that the vectors 5 hat i+6hatj+7hatk,7hati-8hatj+9hatk,3hati+20hatj+5hatk are coplanar.

Examine whether the vectors hati+3hatj+hatk,2hati-hatj-hatk and 7hatj+5hatk are coplanar.

FULL MARKS-VECTOR ALGEBRA-I-EXERCISE 8.2
  1. Verify whether the ratios are direction cosines of some vector or not....

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  2. Find the direction cosines of a vector whose direction ratios are (i) ...

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

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

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

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

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  7. Show that the vectors -hati-2hatj-6hatk,2hati-hatj+hatk" "and -hati+3h...

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

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  9. Show that the following vectors are coplaner. (i) hati-2hatj+3hatk,-2...

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

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

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

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

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

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

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

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

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