Let a,bandcbe there unit vectors such that a×(b×c)=23(b+c). If bis not parallel to c, then the angle between aandbis:
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Represent graphically a displacement of 40 km, 30∘ east of north.
For any two vectors →aand →bwe always have ∣→a→˙b∣≤∣→a∣∣→b∣(Cauchy-Schwartz inequality).
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
Write all the unit vectors in XY−plane˙
Find the vector joining the points P(2,3,0)and Q(1,2,4)directed from P to Q.
Write the direction ratios of the vector →a=i^+j^−2k^and hence calculate its direction cosines.
Find the projection of the a=2i^+3j^+2k^on the b=i^+2j^+k^.
Classify the following measures as scalars and vectors.(i) 10 kg (ii) 2 meters north-west (iii) 40∘(iv) 40 watt (v) 10−19 coulomb (vi)20 m/s2