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

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)).`

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The correct Answer is:
`sqrt(426)`
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If vec(alpha)=2hat(i)-5hat(j)+4hat(k) " and " vec(beta)=hat(i)-4hat(j)+6hat(k), " find " (2vec(alpha)-vec(beta)) . Also find a unit vector in the direction of the vector (2vec(alpha)-vec(beta)) .

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.

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)).

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

Let vec(a)=4hat(i)+3hat(j)-hat(k), vec(b)=5hat(i)+2hat(j)+2hat(k), vec(c)=2hat(i)-2hat(j)-3hat(k) " and "vec(d)=4hat(i)-4hat(j)+3hat(k), " prove that " vec(b)-vec(a) " and " vec(d)-vec(c) are parallel and find the ratio of their moduli.

If vec(a) = 3 hat (i) - 2 hat (j) + hat (k) and vec(b) = hat (i) - 3 hat (j) + 4 hat (k) , find vec(a) xx vec (b) and the area of the parallelogram whose adjacent sides are vec (a) and vec (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)) .

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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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