Vectors

JEE Main Mathematics · 9 questions

All questions, latest first

• 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:20268 April, Shift 2 · Q14
• 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…20266 April, Shift 2 · Q15
• If a= i+ j+ k, b= j- k and c be three vectors such that a × c= b and a · c=3, then c ·( a-2 b) is equal to ____.20266 April, Shift 1 · Q23
• Let O be the origin, O P= a and O Q= b. If R is the point on O P such that O P=5 O R, and M is the point such that OQ=5 RM, then…20265 April, Shift 2 · Q16
• 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 |3 r|^2 is equal to:20265 April, Shift 1 · Q14
• 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