Scalar (dot) product

JEE Main Mathematics · Vectors · 19 questions, latest first

• Let u and v be unit vectors inclined at an acute angle such that | u × v|=(√3)/2. If A=λ u+ v+( u × v), then λ is equal to:20264 April, Shift 2 · Q15
• Let the vectors a=- i+ j+3 k and b= i+3 j+ k. For some λ, μ ∈ R, let c=λ a+μ b. If c ·(3 i-6 j+2 k)=10 and c ·( i+ j+ k)=-2, then…20262 April, Shift 2 · Q14
• 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 an…20262 April, Shift 2 · Q16
• 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:20262 April, Shift 1 · Q14
• For three unit vectors a, b, c satisfying | a- b|^2+| b- c|^2+| c- a|^2=9 and |2 a+k b+k c|=3, the positive value of k is202628 January, Shift 1 · Q14
• Let a vector a=√2 i- j+λ k, λ>0, make an obtuse angle with the vector b=-λ^2 i+4 √2 j+4 √2 k and an angle θ, (π)/6<θ<(π)/2, with…202622 January, Shift 2 · Q24
• Let a= i+2 j+ k and b=2 i+ j- k. Let c be a unit vector in the plane of the vectors a and b and be perpendicular to a. Then such…20258 April, Shift 2 · Q14
• Let a and b be the vectors of the same magnitude such that (| a+ b|+| a- b|)/(| a+ b|-| a- b|)=√2+1. Then (| a+ b|^2)/(| a|^2) is:20257 April, Shift 2 · Q15
• Let the angle θ, 0<θ<(π)/2 between two unit vectors a and b be sin^-1((√65)/9). If the vector c=3 a+6 b+9( a × b), then the value…20257 April, Shift 1 · Q15
• Let the arc AC of a circle subtend a right angle at the centre O. If the point B on the arc AC, divides the arc AC such that…202523 January, Shift 1 · Q13
• Let a and b be two unit vectors such that the angle between them is (π)/3. If λ a+2 b and 3 a-λ b are perpendicular to each…202522 January, Shift 2 · Q13
• Let a= i+2 j+3 k, b=2 i+3 j-5 k and c=3 i- j+λ k be three vectors. Let r be a unit vector along b+ c. If r · a=3, then 3 λ is…20248 April, Shift 2 · Q18
• The set of all α, for which the vectors a=α t i+6 j-3 k and b=t i-2 j-2 α t k are inclined at an obtuse angle for all t ∈ R, is20248 April, Shift 1 · Q18
• For λ>0, let θ be the angle between the vectors a= i+λ j-3 k and b=3 i- j+2 k. If the vectors a+ b and a- b are mutually…20244 April, Shift 2 · Q18
• Let a unit vector which makes an angle of 60^° with 2 i+2 j- k and an angle of 45^° with i- k be C. Then C+(-1/2 i+1/(3 √2)…20244 April, Shift 1 · Q18
• Let a unit vector u=x i+y j+z k make angles (π)/2, (π)/3 and (2 π)/3 with the vectors 1/(√2) i+1/(√2) k, 1/(√2) j+1/(√2) k and…202429 January, Shift 2 · Q15
• The least positive integral value of α, for which the angle between the vectors α i-2 j+2 k and α i+2 α j-2 k is acute, is ____.202427 January, Shift 1 · Q28
• An arc PQ of a circle subtends a right angle at its centre O. The mid point of the arc PQ is R. If O P= u, O R= v and O Q=α u+β…202310 April, Shift 1 · Q17
• Let a=2 i+ j+ k, and b and c be two nonzero vectors such that | a+ b+ c|=| a+ b- c| and b · c=0. Consider the following two…202331 January, Shift 1 · Q77