Maths-
General
Easy

Question

Let stack a with rightwards arrow on top be a unit vector perpendicular to unit vectors stack b with rightwards arrow on top a n d stack c with rightwards arrow on top inclined at an angle a, then stack b with rightwards arrow on top cross times stack c with rightwards arrow on top is

  1. (cosa) stack a with rightwards arrow on top    
  2. (coseca) stack a with rightwards arrow on top    
  3. ( sina) stack a with rightwards arrow on top    
  4. none of these    

The correct answer is: ( sina) stack a with rightwards arrow on top

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Let stack a with rightwards arrow on top comma short rightwards arrow over leftwards arrow short rightwards arrow over leftwards arrow stack b with rightwards arrow on top short rightwards arrow over leftwards arrow short rightwards arrow over leftwards arrow a n d short rightwards arrow over leftwards arrow short rightwards arrow over leftwards arrow short rightwards arrow over leftwards arrow stack c with rightwards arrow on top be three non-coplanar vectors and stack d with rightwards arrow on top be a non-zero vector which is perpendicular to open parentheses stack a with rightwards arrow on top plus stack b with rightwards arrow on top plus stack c with rightwards arrow on top close parentheses and is represented as stack d with rightwards arrow on top equals x open parentheses stack a with rightwards arrow on top cross times stack b with rightwards arrow on top close parentheses plus y open parentheses stack b with rightwards arrow on top cross times stack c with rightwards arrow on top close parentheses plus z open parentheses stack c with rightwards arrow on top cross times stack a with rightwards arrow on top close parentheses. Then

Let stack a with rightwards arrow on top comma short rightwards arrow over leftwards arrow short rightwards arrow over leftwards arrow stack b with rightwards arrow on top short rightwards arrow over leftwards arrow short rightwards arrow over leftwards arrow a n d short rightwards arrow over leftwards arrow short rightwards arrow over leftwards arrow short rightwards arrow over leftwards arrow stack c with rightwards arrow on top be three non-coplanar vectors and stack d with rightwards arrow on top be a non-zero vector which is perpendicular to open parentheses stack a with rightwards arrow on top plus stack b with rightwards arrow on top plus stack c with rightwards arrow on top close parentheses and is represented as stack d with rightwards arrow on top equals x open parentheses stack a with rightwards arrow on top cross times stack b with rightwards arrow on top close parentheses plus y open parentheses stack b with rightwards arrow on top cross times stack c with rightwards arrow on top close parentheses plus z open parentheses stack c with rightwards arrow on top cross times stack a with rightwards arrow on top close parentheses. Then

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Let OPQR is a tetrahedron such that O is origin and stack p with rightwards arrow on top comma short rightwards arrow over leftwards arrow short rightwards arrow over leftwards arrow stack q with rightwards arrow on top comma short rightwards arrow over leftwards arrow short rightwards arrow over leftwards arrow stack r with rightwards arrow on topare position vectors of P, Q, R respectively and a is the angle which OP makes with face PQR then

Hence required angle is 2.

Let OPQR is a tetrahedron such that O is origin and stack p with rightwards arrow on top comma short rightwards arrow over leftwards arrow short rightwards arrow over leftwards arrow stack q with rightwards arrow on top comma short rightwards arrow over leftwards arrow short rightwards arrow over leftwards arrow stack r with rightwards arrow on topare position vectors of P, Q, R respectively and a is the angle which OP makes with face PQR then

Maths-General

Hence required angle is 2.

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