Vector Algebra questions
907 published questions with worked solutions.
- If the foot of the perpendicular drawn from the origin to a plane is M(-1, -2, 2), then the vector equation of the plane is
- If a, b, c are unit vectors such that a+ b+ c= 0, then the value of a b+ b c+ c a is
- | a|= 3, | b|=5, b c=10 and angle between b and c is ( 3 ). If a perpendicular to b c, then value of | a ( b c)| is
- If the area of the parallelogram with a and b as two adjacent sides is 15 sq. units, then the area of the parallelogram having 3...
- The magnitude of the projection of the vector 2 i+ j+ k, on the vector perpendicular to the plane containing the vectors i+ j+ k...
- a = i + j + k , b = j - k , then vector r satisfying a r = b and a r = 3 is
- The magnitude of the projection of the vector 2 i + j + k on the vector perpendicular to the plane containing the vectors i + j +...
- The shortest distance between the lines x-1 2 = y-2 3 = z-3 4 and x-2 3 = y-4 4 = z-5 5 is
- Vectors a and b are such that | a | = 1; | b | = 4 and a b = 2. If c = 2 a b - 3 b , then the angle between b and c is
- Two adjacent sides of a parallelogram are 2 i - 4 j + 5 k and i - 2 j - 3 k , then the unit vector parallel to its diagonal is
- If D, E and F are the mid-points of the sides BC, CA and AB of triangle ABC respectively, then AD + 2 3 BE + 1 3 CF =
- The value of , so that the volume of the parallelepiped formed by i + j + k , j + k and i + j becomes maximum, is
- A vector n is inclined to X-axis at 45^0, Y-axis at 60^0 and at an acute angle to Z-axis. If n is normal to a plane passing...
- The scalar product of the vector i+ j+ k with a unit vector along the sum of the vectors 2 i+4 j-5 k and i+2 j+3 k is equal to 1,...
- If [ ( a+2 b+3 c ) ( b+2 c+3 a ) ] ( c+2 a+3 b )=54, then the value of [ a b c] is
- If the Cartesian equation of a line is 6x – 2 = 3y + 1 = 2z – 2, then the vector equation of the line is
- The volume of parallelepiped, whose coterminus edges are given by u= i+ j+ k, v= i+ j+3 k, w=2 i+ j+ k is 1 cu. units. If is the...
- Let a = i + 3 j - k , b = 3 i - j + 4 k and c = i + 2 j - 2 k , where , IR, be three vectors. If the projection of a on c is 10 3...
- Let a , b and c be vectors of magnitude 2, 3 and 4 respectively. If a is perpendicular to ( b + c ), b is perpendicular to ( c +...
- A unit vector coplanar with i + j + k and 2 i + j + k and perpendicular to i + j - k is
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