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Show that each of the given three vector...

Show that each of the given three vectors is a unit vector: `1/7 (2 hat i + 3 hat j + 6 hat k)`, `1/7(3 hat i - 6 hat j + 2 hat k)`, `1/7 (6 hat i + 2 hat j - 3 hat k)` Also, show they are mutually perpendicular to each other.

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If 3 hat i + 6 hat j + 2 hat k , hat i - 2 hat j + 3 hat k and 5 hat i + 2 hat j + m hat k are coplanar.

Find lambda if the vectors hat i - hat j + hat k , 3 hat i + hat j + 2 hat k and hat i + lambda hat j - 3 hat k are coplanar.

Show that the vectors 2 hat i - 3 hat j + hat k , - 4hati - hat j + 3 hat k and -2 hat i - 4hatj + 4 hat k are coplanar.

Show that the vectors 2 hat i + 3 hat j + 4 hat k and 4 hat i + 6 hat j + 8 hat k are collinear.

Find the angle between the vectors hat i - 2 hat j + 3 hat k and 3 hat i - 2 hat j + hat k .

Find the sum of the vectors veca = hat i - 2 hat j + hat k, vec b = - 2 hat i + 4 hat j + 5 hat k and vec c = hat i - 6 hat j - 7 hat k .

Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k and 2 hat i + 5 hat j - hat k from a triangle in space.

Find the projection of the vector hat i + 3 hat j + 7 hat k on the vector 7 hat i - hat j + 8 hat k .

Show that the points with the position vectors 2 hat i + 6 hat j + 3 hat k, hat i + 2 hat j + 7 hat k and 3 hat i + 10 hat j - hat k are collinear.

Show that the points with position vectors 2 hat i + 6 hat j + 3 hat k , hat i + 2 hat j + 7 hat k and 3 hat i + 10 hat j - hat k are collinear.

NCERT TAMIL-VECTOR ALGEBRA-EXERCISE 10.3
  1. Find the angle between two vectors vec a and vec b with magnitudes sqr...

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  2. Find the angle between the vectors hati-2hatj+3hatkand3hati-2hatj+hatk

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  3. Find the projection of the vector hati-hatj on the vector 7hati+hatj.

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  4. Find the projection of the vector hat i + 3 hat j + 7 hat k on the vec...

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  5. Show that each of the given three vectors is a unit vector: 1/7 (2 hat...

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  6. Find |veca|and|vecb|, if (veca+vecb)*(veca-vecb)=8and|veca|=8|vecb|.

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  7. Evaluate the product (3veca-5vecb)*(2veca+7vecb).

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  8. Find the magnitude of two vectors vecaandvecb , having the same magni...

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  9. Find |vecx| if for a unit vector veca,(vecx-veca)(vecx+veca)=12

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  10. Given veca=2hati+2hatj+3hatk, vecb=-hati+2hatj+hatk and vecc=3hati+hat...

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  11. Show that |veca|vecb+|vecb|veca is perpendicular to |veca|vecb-|vecb|...

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  12. If vec a. vec a = 0 and vec a. vec b = 0 the what can be concluded abo...

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  13. If veca,vecb,vecc are unit vectors such that veca+vecb+vecc=vec0 , fin...

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  14. If either vector veca=vec0orvecb=vec0, , then veca*vecb=0. But the c...

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  15. If either vector A,B,C of a triangle ABC are (1,2,3),(-1,0,0),(0,1,2)...

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  16. Show that the points A(1,2,7), B(2,6,3) and C(3, 10, -1) are collinear...

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  17. Show that the vectors 2hati-hatj+hatk,hati-3hatj-5hatkand3hati-4hatk f...

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  18. If veca is a non zero vector of magnitude 'a' and lambda a nonzero sca...

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