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If a = 3hat(i) + hat(j) + 2hat(k), b = 2...

If `a = 3hat(i) + hat(j) + 2hat(k), b = 2hat(i) - 3hat(j) + 4hat(k)`, then verify that `a xx b` is perpendicular to both a and b.

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The correct Answer is:
`vec(a)xxvec(b) bot vec(b)`
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ARIHANT PRAKASHAN-VECTORS -TOPIC -2 (PRACTICE QUESTIONS) (1 MARK QUESTIONS)
  1. If (vec a times vec b)^2 + (vec a cdot vec b)^2=144, write the value o...

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  2. It the vectors vec(a), vec(b) and vec(c) form the sides vec(BC), vec(C...

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  3. If a = 3hat(i) + hat(j) + 2hat(k), b = 2hat(i) - 3hat(j) + 4hat(k), th...

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  4. If |vec(a)|=3,|vec(b)|=2 and vec(a)*vec(b)=0, then write the value of ...

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  5. Find the component of the vector vec(b) = 8hat(i) + hat(j) in the dire...

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  6. Write a vector normal to (hat(i)+hat(k)) and (hat(i)+hat(j)).

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  7. Find the area of the parallelogram whose diagonals are the vectors 3ha...

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  8. Determine the value of m, for which the following vectors are orthogon...

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  9. Find the value of lambda such that the following vectors are coplanar...

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  10. For what value of lambda, the vectors lambda hat(i) + 3hat(j) + lambda...

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  11. Find the scalar projection of the vector vec a= 3 hat i+6 hat j+9 hat ...

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  12. Determine mu, for which the vector vec(a)=mu(6hat(i)+2hat(j)-3hat(k)) ...

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  13. Show that the vectors 2hat(i) + 3hat(j), 5hat(i) - 5hat(k) and 6hat(j)...

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  14. If vec(a).vec(b) = 0 and vec(a) xx vec(b) = vec(0), then draw the conc...

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  15. If vec(a)xxvec(b)=vec(b)xxvec(c )!=vec(0), then prove that vec(a)+ve...

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  16. What is the angle between the vectors 2hat(i) - hat(j) - hat(k) and ha...

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  17. Determine the area of the parallelogram whose sides are the vectors 2h...

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  18. Using vector method find the area of the triangle with vertices (1, 0,...

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  19. Write the angle between vec(a) and vec(c ), if vec(a)xx(vec(b)xxvec(c ...

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  20. What is (hat(i)-hat(j))*(hat(j)-hat(i)) ?

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