Vector equations

JEE Main Mathematics · Vectors · 28 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
• 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 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 a=2 i-5 j+5 k and b= i- j+3 k. If c is a vector such that 2( a × c)+3( b × c)= 0 and ( a- b) · c=-97, then | c × k|^2 is…202624 January, Shift 2 · Q15
• Let c and d be vectors such that | c+ d|=√29 and c ×(2 i+3 j+4 k)=(2 i+3 j+4 k) × d. If λ_1, λ_2(λ_1>λ_2) are the possible values…202621 January, Shift 1 · Q15
• Let a=- i+2 j+2 k, b=8 i+7 j-3 k and c be a vector such that a × c= b. If c ·( i+ j+ k)=4, then | a+ c|^2 is equal to:202621 January, Shift 1 · Q16
• Let a= i+2 j+ k, b=3 i-3 j+3 k, c=2 i- j+2 k and d be a vector such that b × d= c × d and a · d=4. Then |( a × d)|^2 is equal to…20253 April, Shift 2 · Q24
• Let a= i+ j+ k, b=3 i+2 j- k, c=λ j+μ k and d be a unit vector such that a × d= b × d and c · d=1. If c is perpendicular to a,…20253 April, Shift 1 · Q24
• Let a=2 i-3 j+ k, b=3 i+2 j+5 k and a vector c be such that ( a- c) × b=-18 i-3 j+12 k and a · c=3. If b × c= d, then | a · d| is…20252 April, Shift 2 · Q16
• Let a=2 i- j+3 k, b=3 i-5 j+ k and c be a vector such that a × c= c × b and ( a+ c) ·( b+ c)=168. Then the maximum value of |…202529 January, Shift 1 · Q16
• Between the following two statements: Statement I: Let a= i+2 j-3 k and b=2 i+ j- k. Then the vector r satisfying a × r= a × b…20249 April, Shift 2 · Q17
• Let a=4 i- j+ k, b=11 i- j+ k and c be a vector such that ( a+ b) × c= c ×(-2 a+3 b). If (2 a+3 b) · c=1670, then | c|^2 is equal…20248 April, Shift 2 · Q17
• Let a=9 i-13 j+25 k, b=3 i+7 j-13 k and c=17 i-2 j+ k be three given vectors. If r is a vector such that r × a=( b+ c) × a and r…20248 April, Shift 1 · Q28
• Let a=2 i-3 j+4 k, b=3 i+4 j-5 k and a vector c be such that a ×( b+ c)+ b × c= i+8 j+13 k. If a · c=13, then (24- b · c) is…20246 April, Shift 1 · Q29
• Let a=2 i+5 j- k, b=2 i-2 j+2 k and c be three vectors such that ( c+ i) ×( a+ b+ i)= a ×( c+ i). If a · c=-29, then c ·(-2 i+ j+…20245 April, Shift 2 · Q18
• Let a= i-3 j+7 k, b=2 i- j+ k and c be a vector such that ( a+2 b) × c=3( c × a). If a · c=130, then b · c is equal to ____.20245 April, Shift 1 · Q29
• Let a= i+ j+ k, b=- i-8 j+2 k and c=4 i+c_2 j+c_3 k be three vectors such that b × a= c × a. If the angle between the vector c…20241 February, Shift 2 · Q30
• Let a=3 i+2 j+ k, b=2 i- j+3 k and c be a vector such that ( a+ b) × c=2( a × b)+24 j-6 k and ( a- b+ i) · c=-3. Then | c|^2 is…202431 January, Shift 2 · Q30
• Let a=3 i+ j-2 k, b=4 i+ j+7 k and c= i-3 j+4 k be three vectors. If a vectors p satisfies p × b= c × b and p · a=0, then p ·( i-…202431 January, Shift 1 · Q18
• Let a= i+4 j+2 k, b=3 i-2 j+7 k and c=2 i- j+4 k. If a vector d satisfies d × b= c × b and d · a=24, then | d|^2 is equal to202313 April, Shift 1 · Q9
• Let λ ∈ Z, a=λ i+ j- k and b=3 i- j+2 k. Let c be a vector such that ( a+ b+ c) × c= 0, a · c=-17 and b · c=-20. Then | c ×(λ i+…202312 April, Shift 1 · Q17
• Let a=6 i+9 j+12 k, b=α i+11 j-2 k and c be vectors such that a × c= a × b. If a · c=-12, c ·( i-2 j+ k)=5, then c ·( i+ j+ k) is…20238 April, Shift 1 · Q29
• Let a=2 i-7 j+5 k, b= i+ k and c= i+2 j-3 k be three given vectors. If r is a vector such that r × a= c × a and r · b=0, then |…20231 February, Shift 2 · Q75
• Let: a= i+2 j+3 k, b= i- j+2 k and c=5 i-3 j+3 k be there vectors. If r is a vector such that, r × b= c × b and r · a=0, then 25|…202331 January, Shift 2 · Q67
• If a= i+2 k, b= i+ j+ k, c=7 i-3 j+4 k, r × b+ b × c= 0 and r · a=0. Then r · c is equal to202329 January, Shift 2 · Q78
• Let a=- i- j+ k, a · b=1 and a × b= i- j. Then a-6 b is equal to202325 January, Shift 2 · Q77
• Let a= i+2 j+λ k, b=3 i-5 j-λ k, a · c=7,2 b · c+43=0, a × c= b × c. Then | a · b| is equal to202324 January, Shift 2 · Q86
• Let u= i- j-2 k, v=2 i+ j- k, v · w=2 and v × w= u+λ v. Then u · w is equal to202324 January, Shift 1 · Q77