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Find the position vector of the mid poin...

Find the position vector of the mid point of the line segment joining the points `A(5hat(i) + 3hat(j))` and `B(3hat(i) - hat(j))`.

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Find the position vectors of a point R which divides the line joining two points P and Q whose position vectors are hat(i)+2hat(j)-hat(k)- and - hat(i)+hat(j)-hat(k) respectively, in the ration 2:1 . (i) Internally, (ii) Externally.

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Find the vector equation of a sphere with centre having the position vector hat(i)+hat(j)+hat(k) and radius sqrt(3).

Find the magnitude of the vector (2hat(i) - 3hat(j) - 6hat(k)) + (-hat(i) + hat(j) + 4hat(k)) .

Find the unit vector perpendicular to the plane ABC where the position vectors A, B and C are 2hat(i) - hat(j) + hat(k), hat(i) + hat(j) + 2hat(k) and 2hat(i) + 3hat(k) .