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

If `vec(AB)=2hat(i)-4hat(j)+5hat(k) " and " vec(BC)=hat(i)-2hat(j)-3hat(k)` in parallelogram ABCD, find a unit vector in direction parallel to the diagonal `vec(AC)` of the parallelogram.

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The correct Answer is:
`1/7(3hat(i)-6hat(j)+2hat(k))`
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vec(a)=hat(i)+hat(j)+hat(k) " and " vec(b)=2hat(i)+hat(j)+2hat(k) represent two adjacent sides of a parallelogram. Find unit vectors in directions parallel to the diagonals of the parallelogram.

If vec(a)=hat(i)+2hat(j)-hat(k) " and " vec(b)=3hat(i)+hat(j)-5hat(k) , find a unit vector in a direction parallel to vector (vec(a)-vec(b)) .

If vec(a)=2hat(i)-5hat(j)+3hat(k) " and " vec(b)=hat(i)-2hat(j)-4hat(k) , find the value of abs(3vec(a)+2vec(b)).

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)) .

If vectors vec(alpha)=2hat(i)+3hat(j)-6hat(k) " and " vec(beta)=phat(i)-hat(j)+2hat(k) are parallel, then the value of p is -

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If vec(a)=hat(i)+hat(j)-4hat(k) " and " vec(b)=4hat(i)-hat(j)-2hat(k) , then find (i) a unit vector in the direction of the vector (2vec(a)-vec(b)) and (ii) vector and scalar components of the vector (2vec(a)-vec(b)) along coordinate axes.

If vec(a)=2hat(i)+3hat(j)-4hat(k) " and " vec(b)=hat(i)+2hat(j)+hat(k) , then find (vec(a)+vec(b)) " and " abs(vec(a)+vec(b)).

The sides of a parallelogram are 2hat(i)+4hat(j)-5hat(k) " and " hat(i)+2hat(j)+3hat(k) . Then the unit vector parallel to one of the diagonals is -

If vec(a)=2hat(i)+hat(j)-3hat(k), vec(b)=5hat(i)+4hat(j)+2hat(k) " and " vec(c)=3hat(i)-3hat(j)-2hat(k) , then find the magnitude of the vector vec(a)+vec(b)+2vec(c) and a unit vector in the direction of this vector.

CHHAYA PUBLICATION-VECTOR-EXERCISE - SHORT ANSWER TYPE QUESTIONS
  1. If vec(a)=hat(i)+2hat(j)-hat(k) " and " vec(b)=3hat(i)+hat(j)-5hat(k),...

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  2. Let vec(a)=4hat(i)+3hat(j)-hat(k), vec(b)=5hat(i)+2hat(j)+2hat(k), vec...

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

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  4. If the position vectors of the points A, B C are 3hat(i)-4hat(j)-4hat(...

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  5. If vec(a), vec(b), vec(c) are three given vectors, show that the point...

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

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  7. If the position vectors of the points A, B, C are -2hat(i)+2hat(j)+2ha...

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  8. If the coordinates of the points A, B and C are (2, 6, 3), (1, 2, 7) ...

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  9. The position vectors of three points are (a) -2hat(i)+3hat(j)+5hat(k...

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  10. If the vectors phat(i)-5hat(j)+6hat(k) " and " 2hat(i)-3hat(j)-qhat(k)...

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  11. If the points having position vectors hat(i)+bhat(j)+chat(k), 7hat(i)+...

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  12. The position vecors of the points A and B are 4hat(i)-3hat(j)+5hat(k) ...

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  13. If vec(AB)=2hat(i)-4hat(j)+5hat(k) " and " vec(BC)=hat(i)-2hat(j)-3hat...

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  14. The position vectors of the points A and B are 2vec(a)+vec(b) " and " ...

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  15. Show that the vector hat(i)+hat(j)+hat(k) makes the same angle with th...

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  16. Let D, E, F are the midpoints of the sides bar(BC), bar(CA) " and " ba...

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  17. If vec(AO)+vec(OB)=vec(BO)+vec(OC), show that the points A, B and C ar...

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