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In each of the following show that the g...

In each of the following show that the given vectors are coplanar:
` vec(a) = hat (i) + hat (j) - 6 hat (k) , vec(b) = hat (i) + 3 hat (j) + 4 hat (k) , vec(c) = 2 hat (i) + 5 hat (j) + 3 hat (k) `

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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)

If vec (a) = 2 hat (i) - 3 hat (j) + 4 hat (k) and vec(b) = - 6 hat (i) + 9 hat (j) - 12 hat (k) , then

The scalar projection of vec(a) = 2 hat (i) - 3hat(j) + hat (k) on vec (b) = 3 hat(i) - 6 hat (j) - 2 hat (k)

Find the projection of vector (vec(b)+vec(c )) on vector vec(a) where vec(a) = hat (i) + 2 hat (j) + hat (k) , vec(b) = hat (i) + 3 hat (j) + hat (k) and vec c = hat (i) + hat (k)

If vec (a)= 2 hat (i) - hat (j) + hat (k) and vec(b) = - hat (i) + 3 hat (j) + 4 hat (k) , then value of vec (a). vec(b) is -

If vec (alpha ) = - hat (i) + 2 hat (j) + hat (k) , vec(b) = 3 hat(i) + hat (j) + 2 hat (k) and vec(c ) = 2 hat (i) + hat (j) + 3 hat (k) , find [ vec(c ) vec(a) vec(b)]

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 vectors vec (a) = p hat (i) + 8 hat (j) + 6 hat (k) and vec (b) = - 3 hat (i) + 4 hat (j) + q hat (k) are parallel , find p and q

Find a unit vector perpendicular to both the vector vec(a) = 2 hat(i) + hat(j) - 2 hat(k) and vec(b) = 3 hat (i) - hat (j) + hat (k)

Find the area of triangle (i) drawn on the vectors vec(a) = 6 hat (i) + 2 hat (j) - 3 hat (k) and vec (b) = 4 hat (i) - hat (j) - 2 hat (k)

CHHAYA PUBLICATION-PRODUCTS OF TWO VECTORS-Exercise 2B ( Short answer type questions)
  1. If vec(a) = hat (i) +hat (j) , vec (b) = hat(i) - hat(j) and vec(c )...

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

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  3. If vec (alpha ) = - hat (i) + 2 hat (j) + hat (k) , vec(b) = 3 hat(i) ...

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  4. The vectors which determine the sides of the parallelopiped are given ...

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  5. The vectors which determine the sides of the parallelopiped are given ...

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  6. In each of the following show that the given vectors are coplanar: ...

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  7. In each of the following show that the given vectors are coplanar: ...

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  8. If vec (a) = -2 hat (i) - 2 hat (j) + 4 hat (k) , vec (b) = - 2 hat(i...

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  9. If the vectors x hat (i) - 4 hat (j) + 5 hat (k) , hat (i) + 2 hat (j...

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  10. If the vectors vec (a) = 2 hat (i) - hat (j) + hat (k) , vec ( b) = h...

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  11. The position vectors of four points A,B,C and D are given below . In e...

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  12. The position vectors of four points A,B,C and D are given below . In e...

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  13. If the vectors -4 hat (i)-6 hat (j) - 2 hat (k) , - hat (i) + 4hat (j)...

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  14. If the vectors vec(a) = 2 hat (i) - lambda hat(j) + 3 hat (k), vec(b)...

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  15. Prove that : (vec(a) + vec(b)). { (vec(b)+vec(c))xx (vec(c)+vec(a))}...

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  16. Prove that : vec(a) . { vec(b) xx (vec(c) + vec(d))} = vec(a) . (ve...

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  17. vec (alpha) = lambda hat (i) + hat (j) + 3 hat (k) , " " vec(beta) = ...

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  18. If the vectors ahat (i) + a hat (j) + c hat (k) , hat (i) + hat (k) an...

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  19. Let vec(a) = hat (i) + hat (j) + hat (k) , vec (b) = hat (i) and vec ...

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  20. Find x such that the four points A(3,2,1), B(4,x,5), C(4,2,-2) and D (...

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