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Find the position vector of the mid-poin...

Find the position vector of the mid-point of the vector joining point` P(2,3,4) and Q(4,1,-2)`

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The position vector of mid -poind of the vector joining the points `P(2,3,4) and (Q(4,1-2)` is given by
PV of the mid -point of `(PQ)=(1)/(2)(PV of P+PV of Q)`
`=(1)/(2)[(2hat(i)+3hat(j)+4hat(k))+(4hat(i)+hat(j)-2hat(k))]=(1)/(2)(6hat(i)+4hat(j)+2hat(k))=3hat(i)+2hat(j)+hat(k)`.
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SUBHASH PUBLICATION-VECTOR ALGEBRA -TWO MARKS/THREE MARKS QUESTIONS WITH ANSWERS
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  2. Find the position vectors of a point R which divides the line joining ...

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  3. Find the position vector of the mid-point of the vector joining point ...

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  4. Show that the points A, B and C with position vectors , vec(a)=3hat(i)...

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  5. Find the angle between two vectors a and b with magnitudes sqrt(3) and...

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  6. Find the angle between the vectors hat(i)-2hat(j)+3hat(k) and 3hat(i)-...

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  7. Find the projection of the vector hat(i)-hat(j) on the vector hat(i)+h...

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  8. Find the projection of the vector hat(i)+3hat(j)+7hat(k) on the vector...

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  9. Find |vec(a)| and |vec(b)|, if (vec(a)+vec(b)).(vec(a)-vec(b))=8 and |...

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  10. Evaluate the product (3vec(a)-5vec(b)).(2vec(a)+7vec(b)).

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  11. Find the magnitude of two vectors vec(a) and vec(b) having the same ma...

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  12. Find |x|, if for a unit vector a, (vec(x)-vec(a)).(vec(x)+vec(a))=12.

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

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  14. Show that |a|b+|b| a is perpendicular to |a|b-|b| a for any two non- z...

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  15. If a,b,c are unit vectors such that a+b+c=0, then find the value of a....

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  16. If either a=0,b=0, then a.b=0. But the converse need not to be true . ...

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  17. If the vertices A,B,C of a triangle ABC have position vectors (1,2,3),...

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  18. Show that the points A(1,2,7),B(2,6,3) and C(3,10,-10 are collinear.

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

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  20. Find |vec(a)xxvec(b)|, if a=hat(i) -7hat(j)+7k and b=3hat(i)-2hat(j)+2...

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