Vector Algebra questions
907 published questions with worked solutions.
- Let a = i +5 j + k , b = i +3 j + k and c =- i +2 j -3 k be three vectors such that, | b c |=5 3 and a is perpendicular to b ....
- Let a and b be two vectors such that |2 a +3 b |=|3 a + b | and the angle between a and b is 60°. If 1 8 a is a unit vector, then...
- Let a = i + j +3 k and b =3 i - j + k . If the area of the parallelogram whose adjacent sides are represented by the vectors a...
- Let a = i +2 j - k , b = i - j and c = i - j - k be three given vectors. If r is a vector such that r a = c a and r . b =0, then...
- Let a, b and c be distinct positive numbers. If the vectors a i +a j +c k , i + k and c i +c j +b k are co-planar, then c is...
- If | a |=2, | b |=5 and | a b |=8, then | a . b | is equal to
- If ( a +3 b ) is perpendicular to (7 a -5 b ) and ( a -4 b ) is perpendicular to (7 a -2 b ), then the angle between a and b (in...
- Let the vectors (2+a+b) i +(a+2b+c) j +(b+c) k , (1+b) i +2b j -b k and (2+b) i +2b j +(1-b) k , b,c R be co-planar. Then which...
- Let p =2 i +3 j + k and q = i +2 j + k be two vectors. If a vector r =( i + j + k ) is perpendicular to each of the vectors ( p +...
- If the projection of the vector i +2 j + k on the sum of the two vectors 2 i +4 j -5 k and - i +2 j +3 k is 1, then is equal...
- Let a = i + j + k and b = j - k . If c is a vector such that a c = b and a . c =3, then a .( b c ) is equal to -
- If vectors a_1 =x i - j + k and a_2 = i +y j +z k are collinear, then a possible unit vector parallel to the vector x i +y j +z k...
- Let a , b be unit vectors. If c be a vector such that the angle between a and c is /12, and b = c + 2( c a ), then |6 c |^ 2 is...
- If the shortest distance between the lines r = (- i + 3 k ) + ( i - a j ) and r = (- j + 2 k ) + ( i - j + k ) is 2/3 , then the...
- If the shortest distance between the lines (x − 1)/2 = (y − 2)/3 = (z - 3)/ and (x − 2)/1 = (y − 4)/4 = (z − 5)/5 is 1/ 3 , then...
- Let a and b be two unit vectors such that |( a + b ) + 2( a b )| = 2. If (0, ) is the angle between a and b , then among the...
- The shortest distance between the lines (x + 7)/(−6) = (y − 6)/7 = z and (7 − x)/2 = y − 2 = z − 6 is
- Let a = i - j + 2 k and let b be a vector such that a b = 2 i - k and a b = 3. Then the projection of b on the vector a - b is
- Let ABC be a triangle such that B C = a , C A = b , A B = c , | a | = 6 2 , | b | = 2 3 and b c = 12. Consider the statements :...
- The line of shortest distance between the lines (x − 2)/0 = (y − 1)/1 = z/1 and (x − 3)/2 = (y − 5)/2 = (z − 1)/1 makes an angle...
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