Vector Algebra questions
907 published questions with worked solutions.
- Let a =2 i +3 j +4 k , b = i -2 j -2 k and c =- i +4 j +3 k . If d is a vector perpendicular to both b and c , and a . d =18,...
- Let the vectors u_1 = i + j +a k , u_2 = i +b j + k and u_3 =c i + j + k be coplanar. If the vectors v_1 =(a+b) i +c j +c k , v_2...
- If the point with position vectors i +10 j +13 k , 6 i +11 j +11 k , 9 2 i + j -8 k are collinear, then (19 -6 )^2 is equal to
- The shortest distance between the lines x-4 4 = y+2 5 = z+3 3 and x-1 3 = y-3 4 = z-4 2 is -
- Let a =6 i +9 j +12 k , b = i +11 j -2 k and c be vectors such that a c = a b . If a . c =-12, c .( i -2 j + k )=5, then c .( i +...
- Let a =2 i +7 j - k , b =3 i +5 k and c = i - j +2 k . Let d be a vector which is perpendicular to both a and b , and c . d =12....
- If the points P and Q are respectively the circumcenter and the orthocentre of a , then PA + PB + PC is equal to -
- Let O be the origin and the position vector of the point P be - i -2 j +3 k . If the position vectors of the points A, B and C...
- The shortest distance between the lines x+2 1 = y -2 = z-5 2 and x-4 1 = y-1 2 = z+3 0 is
- If four distinct points with position vectors a , b , c and d are coplanar, then [ a b c ] is equal to
- Let a = i +2 j +3 k and b = i + j - k . If c is a vector such that a . c =11, b .( a c ) = 27 and b . c =- 3| b |, then | a c |^2...
- For any vector a =a_1 i +a_2 j +a_3 k , with 10|a_i|<1, I = 1, 2, 3, consider the following statements: (A) : max...
- Let a be a non-zero vector parallel to the line of intersection of the two planes described by i + j , i + k and i - j , j - k ....
- Let a, b, c be three distinct real numbers, none equal to one. If the vectors a i + j + k , i +b j + k and i + j +c k are...
- Let Z, a = i + j - k and b =3 i - j +2 k . Let c be a vector such that ( a + b ) c = 0 , a . c =-17 and b . c =-20. Then | c ( i...
- Let for a triangle ABC, AB =-2 i + j +3 k , CB = i + j + k and CA =4 i +3 j + k . If > 0 and the area of the triangle ABC is 5 6,...
- Let | a | = 2, | b | = 3 and the angle between the vectors a and b be 4 . Then |( a +2 b ) (2 a -3 b )|^2 is equal to :
- Let a = i +4 j +2 k , b =3 i -2 j +7 k and c =2 i - j +4 k . If a vector d satisfies d b = c b and d . a =24, then | d |^2 is...
- Let a =3 i + j - k and c =2 i -3 j +3 k . If b is a vector such that a = b c and | b |^2=50, then |72-| b + c |^2| is equal to...
- Let S be the set of all ( , ) for which the vectors i - j + k , i +2 j + k and 3 i -4 j +5 k , where - = 5, are coplanar, then _...
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