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Show that the following vectors are copl...

Show that the following vectors are coplaner.
(i)` hati-2hatj+3hatk,-2hati+3hatj-4hatk,-hatj+2hatk`
(ii) `2hati+3hatj+hatk,hati-hatj,7hati+3hatj+2hatk`

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Show that the following vectors are co-planar (ii) 5hati+6hatj+7hatk,7hati-8hatj+9hatk,-3hati+20hatj+5hatk .

Show that the points vectors are 2hati+3hatj-5hatk,3hati+hatj-2hatk and 6hati-5hatj+7hatk are collinear.

Find the angel between the following pairs of vectors 3hati+2hatj-6hatk, 4hati-3hatj+hatkhati-2hatj+3hatk, 3hati-2hatj+hatk

Find the projection of : (i) hati-hatj on Z-axis (ii) hati+2hatj-2hatk on 2hati-hatj+5hatk (iii) 3hati+hatj-hatk on 4hati-hatj+2hatk

Find a set of vectors reciprocal to the set -hati+hatj+hatk,hati-hatj+hatk,hati+hatj+hatk

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

Vectors perpendicular to hati-hatj-hatk and in the plane of hati+hatj+hatk and -hati+hatj+hatk are (A) hati+hatk (B) 2hati+hatj+hatk (C) 3hati+2hatj+hatk (D) -4hati-2hatj-2hatk

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

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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