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Find the value of [ (hat (k)xx hat (j))...

Find the value of ` [ (hat (k)xx hat (j)).hat(i)+hat(j).hat (k)] `

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Show that the vectors are mutually perpendicular hat (i) + 2 hat (j) + hat (k) ,hat (i) + hat (j) - 3 hat (k) and 7 hat (i) - 4 hat (j) + hat (k)

If the vectors x hat (i) - 4 hat (j) + 5 hat (k) , hat (i) + 2 hat (j) + hat (k) and2 hat (i) - hat (j) + hat (k) are coplanar , find the value x

If (2hat (i) + 6 hat (j) + 27 hat (k) )xx (hat (i) + 3hat (j) + p hat (k)) = vec(0) , find p

In each of the following show that the given vectors are coplanar: 4 hat (i) + 2 hat (j) + hat (k) , 2 hat (i) - hat (j) + 3 hat (k) , 8 hat (i) + 7 hat (k)

Find the value of lamda if three vectors vec(a) = 2hat(i) - hat(j) + hat(k), vec(b) = hat(i) + 2hat(j) - 3hat(k) and vec(c) = 3hat(i) + lamda hat(j) + 5hat(k) are coplanar

If the vectors ahat (i) + a hat (j) + c hat (k) , hat (i) + hat (k) and c hat (i) + c hat (j) + b hat (k) be coplanar, show that c^(2) = ab

The vectors which determine the sides of the parallelopiped are given below : hat(i) + hat (j)+ hat(k),hat(k), 3 hat (i)- hat(j) + 2 hat (k)

The vectors which determine the sides of the parallelopiped are given below : hat (i) + hat (j) + hat (k) , hat (i) + 2 hat (j) + 2 hat (k) , hat (i) - 2 hat (j) + 4 hat (k)

If vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec(b) = hat (i) + hat (j) - hat (k) and |vec (a) xx vec(b)| = sqrt(13 m ) then the value of m is -

Find the vector alpha which is perpendicular to both 4 hat (i) + 5 hat (j) - hat (k) and hat (i) - 4 hat (j) + 5 hat (k) and which satisfies the relation alpha . beta = 21 where beta = 3 hat (i)+ 5 hat (j) - hat (k)

CHHAYA PUBLICATION-PRODUCTS OF TWO VECTORS-Exercise 2A ( Short answer type questions)
  1. Let vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec (b) = hat (j) - h...

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  2. Let vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec (b) = hat (j) - h...

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  3. In each of the following find a unit a vector perpendicular to both v...

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  4. In each of the following find a unit a vector perpendicular to both v...

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  5. In each of the following find a unit a vector perpendicular to both v...

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  6. In each of the following find a unit a vector perpendicular to both v...

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  7. If vec(a) = hat (i) + hat (j) - hat (k) , vec (b) = 2 hat (i) - 2 hat ...

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  8. If vec(a) = hat (i) + hat (j) - hat (k) , vec (b) = 2 hat (i) - 2 hat ...

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  9. Be vector method show that the points (2,-3,4),(-2,1,0)and (1,-2,3) ar...

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  10. If vec(alpha) = 2 hat (i) + hat (j) - 3 hat (k) and vec(beta) = hat (i...

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  11. If vec (a) + vec(b) + vec (c ) = vec(0) and |vec(a)| = 6 , |vec (b)| ...

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  12. Prove that , (vec(a) - vec(b)) xx (vec(a) + vec(b)) = 2 ( vec(a) ...

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  13. Prove that , ( vec(a) xx vec(b))^(2) + (vec (a).vec(b))^(2) = |ve...

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  14. Prove that , vec(a) xx ( vec (b) + vec(c)) + vec(b) xx (vec(c) + ...

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  15. Given that vec(a) . vec(b) = 0 and vec(a) xx vec(b) = vec(0) . What ...

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  16. If vec(a) + vec(b) + vec (c ) = vec(0) , show that vec(a) xx vec(b) =...

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  17. Find the value of [ (hat (k)xx hat (j)).hat(i)+hat(j).hat (k)]

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  18. The three vertices of the triangle ABC are A(2,3,5) B(3,5,8) and C(2,...

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  19. Find a unit vector perpendicular to both the vector vec(a) = 2 hat(i)...

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  20. Find a unit vector perpendicular to each of the vectors vec(a) + vec(b...

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