Scalar triple product

JEE Main Mathematics · Vectors · 7 questions, latest first

• Let a= i+ j+ k, b=2 i+4 j-5 k and c=x i+2 j+3 k, x ∈ R. If d is the unit vector in the direction of b+ c such that a · d=1, then…20244 April, Shift 2 · Q17
• Let a= i+2 j+ k, b=3( i- j+ k). Let c be the vector such that a × c= b and a · c=3. Then a ·(( c × b)- b- c) is equal to:202427 January, Shift 1 · Q19
• If four distinct points with position vectors a, b, c and d are coplanar, then [ a b c] is equal to202311 April, Shift 2 · Q17
• Let a= i+2 j+3 k and b= i+ j- k. If c is a vector such that a · c=11, b ·( a × c)=27 and b · c=-√3| b|, then | a × c|^2 is equal…202311 April, Shift 2 · Q29
• Let a=2 i+7 j- k, b=3 i+5 k and c= i- j+2 k. Let d be a vector which is perpendicular to both a and b, and c · d=12. Then (- i+…202310 April, Shift 2 · Q16
• Let the vectors a, b, c represent three coterminous edges of a parallelopiped of volume V. Then the volume of the parallelopiped,…20236 April, Shift 2 · Q18
• Let v=α i+2 j-3 k, w=2 α i+ j- k and u be a vector such that | u|=α>0. If the minimum value of the scalar triple product [ u v w]…20231 February, Shift 1 · Q90