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Find the component of the vector vec(b) ...

Find the component of the vector `vec(b) = 8hat(i) + hat(j)` in the direction of the vector `vec(a) = hat(i) + 2hat(j) - 2hat(k)`.

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The correct Answer is:
`(10(hat(i)+2hat(j)-2hat(k)))/(9)`
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Resolve the vector vec(b) = hat(i) + hat(j) + hat(k) into vectors parallel and perpendicular to the vector vec(a) = hat(i) + hat(j) .

ARIHANT PRAKASHAN-VECTORS -TOPIC -2 (PRACTICE QUESTIONS) (1 MARK QUESTIONS)
  1. If a = 3hat(i) + hat(j) + 2hat(k), b = 2hat(i) - 3hat(j) + 4hat(k), th...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. (2hat(i)-4hat(j))*(hat(i)+hat(j)+hat(k))= . . . .

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

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