Statement 1: `| vec a|=3,| vec b|= 4 a n d | vec a+ vec b|=5,t h e n| vec a- vec b|=5.` Statement 2: The length of the diagonals of a rectangle is the same.

Statement - I: If abs(vec(a))=3, abs(vec(b))=4 " and " abs(vec(a)+vec(b))=5 " then " abs(vec(a)-vec(b))=5 . Statement - II: The length of the diagonals of a rectangle is same.

If | vec a|=5,| vec a- vec b|=8 and | vec a+ vec b|=10 , then find | vec b|dot

If | vec a|=2| vec b|=5 and | vec axx vec b|=8, then find the value of vec a . vec bdot

Statement 1: If | vec a+ vec b|=| vec a- vec b| , then vec a and vec b are perpendicular to each other. Statement 2: If the diagonal of a parallelogram are equal magnitude, then the parallelogram is a rectangle. Which of the following Statements is/are correct ?

A parallelogram is constructed on 3 vec a+ vec ba n d vec a-4 vec b ,w h e r e| vec a|=6a n d| vec b|=8,a n d vec aa n d vec b are anti-parallel. Then the length of the longer diagonal is 40 b. 64 c. 32 d. 48

A parallelogram is constructed on 3 vec a+ vec ba n d vec a-4 vec b ,w h e r e| vec a|=6a n d| vec b|=8,a n d vec aa n d vec b are anti-parallel. Then the length of the longer diagonal is 40 b. 64 c. 32 d. 48

Given | vec a|=| vec b|=1a n d| vec a+ vec b|=sqrt(3). If vec c is a vector such that vec c- vec a-2 vec b=3( vec axx vec b), then find the value of vec c. vec b

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c . Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] ; then vec d equally inclined to vec a , vec b and vec c . (a) statement 1 is true but statement 2 is false. (b) statement 2 is true but statement 1 is false. (c)both the statements are true. (d) both the statements are false.

Statement 1: vec a=3 vec i+p vec j+3 vec k and vec b=2 vec i+3 vec j+q vec k are parallel vectors if p=9//2a n dq=2. Statement 2: if vec a=a_1 vec i+a_2 vec j+a_3 vec ka n d vec b=b_1 vec i+b_2 vec j+b_3 vec k are parallel, then (a_1)/(b_1)=(a_2)/(b_2)=(a_3)/(b_3)dot Which of the following Statements is/are correct ?

Show that | vec a| vec b+| vec b| vec a is a perpendicular to | vec a| vec b-| vec b| vec a , for any two non-zero vectors vec aa n d vec bdot