Let a → ,   b → and c → be three non - coplanar unit vectors such that the angle between every pair of them is π 3 . If a →   ×   b → +   b →   ×   c → = p a → + q b → + r c → , where p, q and…

Question

Let a &#8594; , &#160; b &#8594; and c &#8594; be three non - coplanar unit vectors such that the angle between every pair of them is &#960; 3 . If a &#8594; &#160; &#215; &#160; b &#8594; + &#160; b &#8594; &#160; &#215; &#160; c &#8594; = p a &#8594; + q b &#8594; + r c &#8594; , where p, q and r are scalars, then the value of p 2 + 2 q 2 + r 2 q 2 &#160; is _______

Aicharya · Accepted Answer

a &#8594; = b &#8594; = &#160; c &#8594; = 1 a &#8594; &#160; &#215; &#160; b &#8594; + &#160; b &#8594; &#160; &#215; &#160; c &#8594; = p a &#8594; + q b &#8594; + r c &#8594; a &#8594; &#160; . &#160; b &#8594; &#160; &#215; &#160; c &#8594; = p + q &#160; a &#8594; &#160; . &#160; b &#8594; + r a &#8594; &#160; . &#160; c &#8594; And a &#8594; &#160; &#160; b &#8594; &#160; &#160; c &#8594; = 1 2 p + q 2 + r 2 = a &#8594; &#160; b &#8594; &#160; c &#8594; .......(i) p 2 + q + r 2 = 0 ......(ii) p 2 + q 2 + r = a &#8594; &#160; b &#8594; &#160; c &#8594; ......(iii) &#8658; p = r = &#160; - q p 2 + 2 q 2 + r 2 q 2 = 4

Let a → ,   b → and c → be three non - coplanar unit vectors such that the angle…

Solution

Let a &#8594; , &#160; b &#8594; and c &#8594; be three non - coplanar unit vectors such that the angle…

Solution

Let a → , b → and c → be three non - coplanar unit vectors such that the angle…