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.

Find | vec a|a n d| vec b|,if( vec a+ vec b)dot( vec a- vec b) = 8 , | vec a|=8| vec b|dot

If | vec a|+| vec b|=| vec c|a n d vec a+ vec b= vec c , then find the angle between vec aa n d vec bdot

If |vec(a)| = 13, |vec(b)| = 5 and vec(a) cdot vec(b) = 60 then |vec(a) xx vec(b)| is

Find |vec a| and |vec b| if (vec a + vec b).(vec a - vec b) = 3 and 2|vec b| = |vec a| .

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 a . 40 b. 64 c. 32 d. 48

Prove that [ vec a, vec b, vec c + vec d] = [ vec a, vec b, vec c] + [ vec a, vec b , vec d] .

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 dot vec b

Statement 1: If vec A=2 hat i+3 hat j+6 hat k , vec B= hat i+ hat j-2 hat ka n d vec C= hat i+2 hat j+ hat k , then | vec Axx( vec Axx( vec Axx vec B)). vec C|=243 Statement 2: | vec Axx( vec Axx( vec Axx vec B)). vec C|=| vec A|^2|[ vec A vec B vec C]| a. Statement 1 and Statement 2 , both are true and Statement 2 is the correct explanation for Statement 1. b. Statement 1 and Statement 2 , both are true and Statement 2 is not the correct explanation for Statement 1. c. Statement 1 is true but Statement 2 is false. c. Statement 2 is true but Statement 1 is false.

Column I, Column II If | vec a|=| vec b|=| vec c| , angel between each pair of vecrtor is pi/3 and | vec a+ vec b+ vec c|=sqrt(6),t h e n2| vec a| is equal to, p. 3 If vec a is perpendicular to vec b+ vec c , vec b is perpendicular to vec c+ vec a , vec c is perpendicular to vec a+ vec b ,| vec a|=2,| vec b|=3a n d| vec c|=6,t h e n| vec a+ vec b+ vec c|-2 is equal to, q. 2 vec a=2 hat i+3 hat j- hat k , vec b=- hat i-4 hat k , vec c= hat i+ hat j+ hat ka n d vec d=3 hat k+2 hat j+ hat k ,t h e n1/7( hat axx hat b)dot( hat cxx hat d) is equal to, r. 4 If | vec a|=| vec b|=| vec c|=2a n d vec adot vec b= vec bdot vec c= vec cdot vec a=2,t h e n[ vec a vec b vec c]cos 45^0 is equal to, s. 5

Let the vectors vec aa n d vec b be such that | vec a|=3| vec b|=(sqrt(2))/3,t h e n vec axx vec b is a unit vector, if the angel between vec aa n d vec b is?