Area of parallelogram and triangle

JEE Main Mathematics · Vectors · 12 questions, latest first

• 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
• Let a=2 i+α j+ k, b=- i+ k, c=β j- k, where α and β are integers and α β=-6. Let the values of the ordered pair ( α, β ), for…20249 April, Shift 2 · Q18
• Let O A=2 a, O B=6 a+5 b and O C=3 b, where O is the origin. If the area of the parallelogram with adjacent sides O A and O C is…20249 April, Shift 1 · Q17
• Let three vectors a=α i+4 j+2 k, b=5 i+3 j+4 k, c=x i+y j+z k form a triangle such that c= a- b and the area of the triangle is 5…20249 April, Shift 1 · Q18
• If A(3,1,-1), B(5/3, 7/3, 1/3), C(2,2,1) and D(10/3, 2/3, -1/3) are the vertices of a quadrilateral A B C D, then its area is20246 April, Shift 1 · Q19
• If A(1,-1,2), B(5,7,-6), C(3,4,-10) and D(-1,-4,-2) are the vertices of a quadrilateral A B C D, then its area is:20245 April, Shift 1 · Q18
• Let ABC be a triangle of area 15 √2 and the vectors AB= i+2 j-7 k, BC=a i+b j+c k and A C=6 i+d j-2 k, d>0. Then the square of…20244 April, Shift 1 · Q30
• Let A(2,3,5) and C(-3,4,-2) be opposite vertices of a parallelogram ABCD. If the diagonal B D= i+2 j+3 k, then the area of the…202430 January, Shift 1 · Q17
• Let O A= a, O B=12 a+4 b and O C= b, where O is the origin. If S is the parallelogram with adjacent sides OA and OC, then (area…202429 January, Shift 2 · Q16
• Let for a triangle A B C, AB=-2 i+ j+3 k; CB=α i+β j+γ k; CA=4 i+3 j+δ k If δ>0 and the area of the triangle ABC is 5 √6, then C…202313 April, Shift 2 · Q18
• The area of the quadrilateral A B C D with vertices A(2,1,1), B(1,2,5), C(-2,-3,5) and D(1,-6,-7) is equal to20238 April, Shift 2 · Q15
• A(2,6,2), B(-4,0, λ), C(2,3,-1) and D(4,5,0),|λ| ≤ 5 are the vertices of a quadrilateral A B C D. If its area is 18 square units,…20231 February, Shift 1 · Q89