यदि `vec(A)` तथा `vec(B)` का परिमाण क्रमशः 3 व 4 हो इनके बीच कोण `theta` हो तो `theta` के किस मान के लिए `vec(A)xxvec(B)` का परिमाण (i) शून्य (ii) 12 (iii) 6 होगा

If sin 5 theta^@=cos 20^@ (0^@ यदि sin 5 theta^@=cos 20^@ (0^@< theta <90^@) हो, तो theta का मान क्या होगा ?

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?

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?

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?

If |vec A|=2 and | vec B| =4 , then match the relations in colum I with theange theta between vec A and vec B in column II. Column I , Column II (a) vec A.vec B=0 , (i) theta =0 (b) vec A . Vec B= + 8 , (ii) theta =90^@ (c ) vec A .vec B =4 , (iii) theta =180^@ (d) vec A .vec B =- 8 , (iv) theta =60^@ .

If vec A = 3hat i + 4hat j + 5hat k and vec b = 5hat i-6hat j + 2hat k find (i) (vec A + vec B) xx (vec A-vec B) (ii) (vec A + case B) * (case A-case B)