Linear dependence, collinearity and coplanarity

JEE Main Mathematics · Vectors · 11 questions, latest first

• Let a= i+2 j+3 k, b=3 i+ j- k and c be three vectors such that c is coplanar with a and b. If the vector c is perpendicular to b…202524 January, Shift 1 · Q13
• Let a, b and c be three non-zero vectors such that b and c are non-collinear. If a+5 b is collinear with c, b+6 c is collinear…202429 January, Shift 1 · Q17
• Let S be the set of all (λ, μ) for which the vectors λ i- j+ k, i+2 j+μ k and 3 i-4 j+5 k, where λ-μ=5, are coplanar, then Σ_(λ,…202315 April, Shift 1 · Q16
• Let a, b, c be three distinct real numbers, none equal to one. If the vectors a i+ j+ k, i+b j+ k and i+ j+c k are coplanar, then…202312 April, Shift 1 · Q16
• Let the vectors u_1= i+ j+a k, u_2= i+b j+ k and u_3=c i+ j+ k be coplanar. If the vectors v_1=(a+b) i+c j+c k, v_2=a i+(b+c) j+a…20238 April, Shift 2 · Q16
• If the points with position vectors α i+10 j+13 k, 6 i+11 j+11 k, 9/2 i+β j-8 k are collinear, then (19 α-6 β)^2 is equal to20238 April, Shift 1 · Q17
• The sum of all values of α, for which the points whose position vectors are i-2 j+3 k, 2 i-3 j+4 k,(α+1) i+2 k and 9 i+(α-8) j+6…20236 April, Shift 2 · Q17
• Let the position vectors of the points A, B, C and D be 5 i+5 j+2 λ k, i+2 j+3 k,-2 i+λ j+4 k and - i+5 j+6 k. Let the set S={λ ∈…20236 April, Shift 1 · Q15
• If the vectors a=λ i+μ j+4 k, b=-2 i+4 j-2 k and c=2 i+3 j+ k are coplanar and the projection of a on the vector b is √54 units,…202329 January, Shift 1 · Q75
• Let a, b and c be three non-zero non-coplanar vectors. Let the position vectors of four points A, B, C and D be a- b+ c, λ a-3…202329 January, Shift 1 · Q85
• If the four points, whose position vectors are 3 i-4 j+2 k, i+2 j- k,-2 i- j+3 k and 5 i-2 α j+4 k are coplanar, then α is equal…202325 January, Shift 2 · Q78