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If vec(a)=hat(i)+hat(j) " and " vec(b)=4...

If `vec(a)=hat(i)+hat(j) " and " vec(b)=4hat(i)-hat(j)`, find a unit vector in the direction of the vector `(2vec(a)-vec(b))`, also find vector and scalar components of `(2vec(a)-vec(b))` along two coordinates axes.

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The correct Answer is:
`1/sqrt(13)(-2hat(i)+3hat(j)) " and " -2hat(i), 3hat(j) " and " -2, 3`
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If vec(a)=2hat(i)+5hat(j)-2hat(k) " and " vec(b)=hat(i)-hat(j)+hat(k) , then find (i) vec(a)+vec(b) " and " 2vec(a)-3vec(b) " " (ii)abs(vec(a)+vec(b)) " and " abs(vec(a)-2vec(b)) (iii) a unit vector in the direction (vec(a)+vec(b)) (iv) vector and scalar components of the vector (2vec(a)-3vec(b)) along the coordinate axes.

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If vec(a)=hat(i)+hat(j)+hat(k), vec(b)=2hat(i)-hat(j)+3hat(k) " and " vec(c)=hat(i)-2hat(j)+hat(k) find a unit vector in a direction parallel to vector (2vec(a)-vec(b)+3vec(c)) .

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CHHAYA PUBLICATION-VECTOR-EXERCISE - VERY SHORT ANSWER TYPE QUESTIONS
  1. Define a vector from the geometrical concept.

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  2. Write two different vectors having the same magnitude.

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  3. Write two different vectors having the same direction.

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  4. Define the position vector of a point with respect to an origin. If ve...

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  5. Define a vector and a unit vector. Find in terms of vector vec(a) a un...

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  6. If vec(a)=2hat(i)-5hat(j)+3hat(k) " and " vec(b)=hat(i)-2hat(j)-4hat(k...

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  7. If vec(a)=2hat(i)+3hat(j)-4hat(k) " and " vec(b)=hat(i)+2hat(j)+hat(k)...

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  8. If vec(alpha)=2hat(i)-5hat(j)+4hat(k) " and " vec(beta)=hat(i)-4hat(j)...

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  9. Show that the vectors -hat(i)+hat(j), -4hat(i)-6hat(j) " and " 5hat(i)...

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  10. The position vectors of the points A, B and C are -5hat(i)+hat(j), 5ha...

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  11. Using vector method show that the points A(-5,7), B(-4,5) and C(1, -5)...

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  12. If vec(a)=hat(i)+hat(j) " and " vec(b)=4hat(i)-hat(j), find a unit vec...

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  13. The position vectors of two given points P and Q are 8hat(i)+3hat(j) "...

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  14. If vec(a)=4vec(i)-3hat(j) " and " vec(b)=-2hat(i)+5hat(j) are the posi...

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  15. Find the vector from the origin to the intersection of the medians of ...

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  16. (i) Determine the value of p for which the vectors phat(i)-5hat(j) " a...

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  17. The position vectors of the points A and B are 3hat(i)-hat(j)+7hat(k) ...

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