Vector Algebra questions
907 published questions with worked solutions.
- Let ABCDEF be a regular hexagon in the x-y plane and AB = 4 i . Then CD is equal to
- Let u= i+ j, v= i- j and w= i+2 j+3 k. If n is a unit vector such that u n=0 and v n=0 then | w n| is equal to
- The ratio in which the line segment joining the points whose position vectors are 2 i-4 j-7 k and -3 i+5 j-8 k is divided by the...
- The value of so that the volume of the parallelopiped formed by the vectors i+ j+ k, j+ k and i+ k becomes minimum, is
- Let c = a + b + , a b where a and b are unit vectors such that a b = 0. Then
- Which of the following is/are equal to ( u v) w?
- For the vectors a, b, c and d which of the following is/are meaningful if and represent scalar and vector products respectively?
- Let a= i- k, b=x i+ j+(1-x) k and c=y i+x j+(1-x-y) k. Then [ a b c] depends on
- If a, b and c are three nonzero noncoplanar vectors and p= b- b a | a|^2 a, q= b+ b a | a|^2 a, r= c- c a | a|^2 a+ b c | c|^2 p,...
- The value of ( a i)^2+( a j)^2+( a k)^2 is equal to
- ( a b) a b+ a b ( a b) is equal to
- *(In (iii) the book prints =2 a+3 b+ c for the third vector, which is the same as .)* Column I: (i) If z-2i 3 then the maximum...
- In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than...
- If | a| = 3, | b| = 4, | c| = 5, a ( b + c), b ( c + a) and c ( a + b) then 2 ,| a + b + c| is equal to _____.
- STATEMENT-1: [ , b c ; ; c a ; ; a b ,] = 0. STATEMENT-2: If p, q, r are linearly dependent vectors then they are coplanar.
- Given two straight lines whose equations are x-3 1 = y-5 -2 = z-7 1 and x+1 7 = y+1 -6 = z+1 1 . STATEMENT-1: The line of...
- If a, b and c are unit vectors and the angles between a, b; b, c and c, a are 6 , 3 and 4 respectively then | a + b + c| is
- If a + b + c = 0 then a b is equal to
- Let the vectors PQ , QR , RS , ST , TU and UP represent the sides of a regular hexagon. STATEMENT-1: PQ ( RS + ST ) 0...
- If a and b are two perpendicular unit vectors then a ( a b) is equal to
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