Let PR=3i^+j^−2k^andSQ=i^−3j^−4k^determine diagonals of a parallelogram PQRS,andPT=i^+2j^+3k^be another vector. Then the volume of the parallelepiped determine by the vectors PT, PQand PSis5b. 20c. 10d. 30
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Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (5,7).
Find the unit vector in the direction of the sum of the vectors, →a=2i^+2j^−5k^and →b=2i^+j^+3k^.
Find the unit vector in the direction of vector PQ, where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.
Given that ab˙=0and a×b=0. What can you conclude about the vectors aand b.
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are 2(a+b)and (a−3b)externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ
Answer the following as true or false.(i) aand −aare collinear.(ii) Two collinear vectors are always equal in magnitude.(iii) Two vectors having same magnitude are collinear.(iv) Two collinear vectors having the same magnitude
Show that ∣a∣b+∣∣b∣∣ais perpendicular to ∣a∣b−∣∣b∣∣a, for any two nonzero vectors a and b.