Vector (cross) product

JEE Main Mathematics · Vectors · 19 questions, latest first

• Let a=2 i+ j-2 k, b= i+ j and c= a × b. Let d be a vector such that | d- a|=√11,| c × d|=3 and the angle between c and d is…202624 January, Shift 1 · Q15
• Let a, b, c be three vectors such that a × b=2( a × c). If | a|=1,| b|=4,| c|=2, and the angle between b and c is 60^°, then | a…202623 January, Shift 2 · Q16
• Let a=2 i- j+ k and b=λ j+2 k, λ ∈ Z be two vectors. Let c= a × b and d be a vector of magnitude 2 in y z -plane. If | c|=√53,…202622 January, Shift 2 · Q14
• For a triangle ABC, let p= B C, q= C A and r= B A. If | p|=2 √3,| q|=2 and cos θ=1/(√3), where θ is the angle between p and q,…202621 January, Shift 2 · Q16
• Let a be a unit vector perpendicular to the vectors b= i-2 j+3 k and c=2 i+3 j- k, and makes an angle of cos^-1(-1/3) with the…202529 January, Shift 2 · Q14
• Let a= i+ j+ k, b=2 i+2 j+ k and d= a × b. If c is a vector such that a · c=| c|, | c-2 a|^2=8 and the angle between d and c is…202528 January, Shift 1 · Q24
• Let a=6 i+ j- k and b= i+ j. If c is a is vector such that | c| ≥ 6, a · c=6| c|,| c- a|=2 √2 and the angle between a × b and c…20246 April, Shift 2 · Q19
• Consider three vectors a, b, c. Let | a|=2,| b|=3 and a= b × c. If α ∈[0, (π)/3] is the angle between the vectors b and c, then…20245 April, Shift 2 · Q19
• Let a and b be two vectors such that | a|=1,| b|=4, and a · b=2. If c=(2 a × b)-3 b and the angle between b and c is α, then 192…202431 January, Shift 1 · Q30
• Let a and b be two vectors such that | b|=1 and | b × a|=2. Then |( b × a)- b|^2 is equal to202430 January, Shift 2 · Q18
• Let a= i+α j+β k, α, β ∈ R. Let a vector b be such that the angle between a and b is (π)/4 and | b|^2=6. If a · b=3 √2, then the…202430 January, Shift 2 · Q19
• Let a=a_1 i+a_2 j+a_3 k and b=b_1 i+b_2 j+b_3 k be two vectors such that | a|=1, a · b=2 and | b|=4. If c=2( a × b)-3 b, then the…202430 January, Shift 1 · Q18
• Let | a|=2,| b|=3 and the angle between the vectors a and b be (π)/4. Then |( a+2 b) ×(2 a-3 b)|^2 is equal to202313 April, Shift 2 · Q17
• Let a=3 i+ j- k and c=2 i-3 j+3 k. If b is a vector such that a= b × c and | b|^2=50, then |72-| b+ c|^2| is equal to ____.202313 April, Shift 1 · Q28
• Let a be a non-zero vector parallel to the line of intersection of the two planes described by i+ j, i+ k and i- j, j- k. If θ is…202311 April, Shift 1 · Q11
• Let a=2 i+3 j+4 k, b= i-2 j-2 k and c=- i+4 j+3 k. If d is a vector perpendicular to both b and c, and a · d=18, then | a × d|^2…20236 April, Shift 1 · Q16
• Let a, b, c be three vectors such that | a|=√31, 4| b|=| c|=2 and 2( a × b)=3( c × a). If the angle between b and c is (2 π)/3,…202331 January, Shift 2 · Q88
• Let a and b be two vectors such that | a|=√14,| b|=√6 and | a × b|=√48. Then ( a · b)^2 is equal to ____.202331 January, Shift 1 · Q87
• Let a and b be two vectors, Let | a|=1,| b|=4 and a · b=2. If c=(2 a × b)-3 b, then the value of b · c is202330 January, Shift 2 · Q76