Vector Algebra questions
907 published questions with worked solutions.
- Let the vectors a = - i + j + 3 k and b = i + 3 j + k. For some λ, μ ∈ ℝ, let c = a + b. If c (3 i - 6 j + 2 k) = 10 and c ( i +...
- Two adjacent sides of a parallelogram PQRS are given by PQ = j + k and PS = i - j. If the side PS is rotated about the point P by...
- If a and b are two vectors such that | a| = 2 and | b| = 3, then the maximum value of 3|3 a + 2 b| + 4|3 a − 2 b| is:
- The shortest distance between the lines r= ( 13 i+2 j+ 83 k )+ (2 i-5 j+6 k) and r= (- 23 i- 13 k )+ ( j- k), λ,μ∈ℝ, is:
- Let û and v̂ be unit vectors inclined at an acute angle such that | u v|= 3 2. If A= u+ v+( u v), then λ is equal to:
- Let O be the origin, OP = a and OQ = b. If R is the point on OP such that OP =5 OR , and M is the point such that OQ =5 RM , then...
- Let a= 7 i+ j- k and b= j+2 k. If r is a vector such that r a+ a b= 0 and r a=0, then |3r|² is equal to:
- The shortest distance between the lines x-4 1= y-3 2= z-2 -3 and x+2 2= y-6 4= z-5 -5 is:
- Let a=2 i+3 j+3 k and b=6 i+3 j+3 k. Then the square of the area of the triangle with adjacent sides determined by the vectors (2...
- If a= i+ j+ k, b= j- k and c are three vectors such that a c= b and a c=3, then c ( a-2 b) is equal to _______.
- Let a=4 i- j+3 k, b=10 i+2 j- k and a vector c be such that 2( a b)+3( b c)= 0. If a c=15, then c ( i+ j-3 k) is equal to:
- Let the foot of perpendicular from the point (λ, 2, 3) on the line x-4 1= y-9 2= z-5 1 be the point (1, μ, 2). Then the distance...
- Between the following two statements : Statement-I : Let a⃗ = î + 2ĵ − 3k̂ and b⃗ = 2î + ĵ − k̂. Then the vector r⃗ satisfying a⃗...
- Let a⃗ = 2î + αĵ + k̂, b⃗ = −î + k̂, c⃗ = β ĵ − k̂, where α and β are integers and αβ = −6. Let the values of the ordered pair...
- Let OA = 2 a, OB = 6 a + 5 b and OC = 3 b, where O is the origin. If the area of the parallelogram with adjacent sides OA and OC...
- The shortest distance between the line x-3 4 = y+7 -11 = z-1 5 and x-5 3 = y-9 -6 = z+2 1 is
- Let three vectors a⃗ = αî + 4ĵ + 2k̂, b⃗ = 5î + 3ĵ + 4k̂, c⃗ = xî + yĵ + zk̂ form a triangle such that c⃗ = a⃗ − b⃗ and the area...
- Let a = i + 2 j + k, b = 3( i - j + k). Let c be the vector such that a c = b and a c = 3. Then a (( c b) - b - c) is equal to :
- If the shortest distance between the lines x-4 1 = y+1 2 = z -3 and x- 2 = y+1 4 = z-2 -5 is 6 5 , then the sum of all possible...
- The least positive integral value of α, for which the angle between the vectors i - 2 j + 2 k and i + 2 j - 2 k is acute, is...
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