`vec(a)` and `vec(b)` are any two vectors. Prove that`|vec(a)+vec(b)|le|vec(a)|+|vec(b)|`
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Answer the following : (i) Can 2 similar vectors of different magnitude yield a zero resultant? Can 3 yield? (ii) Can vec(a)+vec(b)=vec(a)-vec(b) ? (iii) If vec(a)+vec(b)=vec(c) & |vec(a)|+|vec(b)|=|vec(c)| . What further information you can have about these vectors. (iv) If vec(a) & vec(b) are two non zero vectors such that |vec(a)+vec(b)|=|vec(a)+vec(b)| , then what is the angle between vec(a) & vec(b) . (v) Time has a magnitude & direction. Is it a vector? (iv) When will vec(a)xxvec(b)=vec(a).vec(b) ? (vii) Does the unit vectors vec(i), vec(j) & vec(k) have units?
For any two vectors vec(a) and vec(b) , we always have |vec(a)+vec(b)|le|vec(a)|+|vec(b)| (triangle inequality).
Let vec(a),vec(b) and vec( c ) be unit vectors such that vec(a).vec(b)=vec(a).vec( c )=0 and the angle between vec(b) and vec( c ) is (pi)/(6) . Prove that vec(a)=+-2(vec(b)xx vec( c )) .
vec(a),vec(b) and vec( c ) are non zero vectors. (vec(a)xx vec(b))xx vec( c )=(1)/(3)|vec(b)||vec( c )|vec(a) . If the acute angle between the vectors vec(b) and vec( c ) is theta then sin theta = ……………
vec(a),vec(b) and vec( c ) are three vector vec(a)ne0 and |vec(a)|=|vec( c )|=1,|vec(b)|=4,|vec(b)xx vec( c )|=sqrt(15) . If vec(b)-2vec( c )=lambda vec(a) then the value of lambda is ………….
Find |vec(a)-vec(b)| , if two vectors vec(a) and vec(b) are such that |vec(a)|=2,|vec(b)|=3 and vec(a).vec(b)=4 .
Let vec(A), vec(B) and vec(C) , be unit vectors. Suppose that vec(A).vec(B)=vec(A).vec(C)=0 and the angle between vec(B) and vec(C) is pi/6 then
Let vec(a),vec(b) and vec( c ) be three unit vectors such that vec(a),+vec(b)+vec( c )=vec(0) . If lambda=vec(a)*vec(b)+vec(b)*vec( c )+vec( c )*vec(a) and vec(d)=vec(a)xx vec(b)+vec(b)xx vec( c )+vec( c )xx vec(a) then the ordered pair (lambda, vec(d)) is equal to :
Let vec(a),vec(b) and vec( c ) be three vectors such that |vec(a)|=3,|vec(b)|=4,|vec( c )|=5 and each one the them being perpendicular to the sum of the other two, find |vec(a)+vec(b)+vec( c )| .
vec(a),vec(b) and vec( c ) are unit vectors vec(a)xx(vec(b)xx vec( c ))=(vec(b))/(2) . The vector vec(a) makes the angle ………, …… with vec(b) and vec( c ) respectively.
KUMAR PRAKASHAN-VECTOR ALGEBRA -Practice Paper - 10 (Section-D)