Let a → = i ^ + 5 j ^ + α k ^ ,   b → = i ^ + 3 j ^ + β k ^ and c → = - i ^ + 2 j ^ - 3 k ^ be three vectors such that, | b → × c → | = 5 3 and a → is perpendicular to b → . Then the greatest amongst the values of | a → | 2 is…

Question

Let a &#8594; = i ^ + 5 j ^ + &#945; k ^ , &#160; b &#8594; = i ^ + 3 j ^ + &#946; k ^ and c &#8594; = - i ^ + 2 j ^ - 3 k ^ be three vectors such that, | b &#8594; &#215; c &#8594; | = 5 3 and a &#8594; is perpendicular to b &#8594; . Then the greatest amongst the values of | a &#8594; | 2 is ________.

Aicharya · Accepted Answer

a &#8594; &#183; b &#8594; = 0 1 + 15 + &#945; &#946; = 0 &#945; &#946; = - 16 &#160; &#160; &#160; &#160; . . . ( 1 ) Also, b &#8594; &#215; c &#8594; 2 = 75 10 + &#946; 2 &#183; 14 - 5 - 3 &#946; 2 = 75 5 &#946; 2 + 30 &#946; + 40 = 0 &#946; = - 4 , &#160; - 2 &#945; = 4 , &#160; 8 a &#8594; m a x 2 = 26 + &#945; 2 m a x = 90

Let a → = i ^ + 5 j ^ + α k ^ ,   b → = i ^ + 3 j ^ + β k ^ and c → = - i ^…

Solution

Let a &#8594; = i ^ + 5 j ^ + &#945; k ^ , &#160; b &#8594; = i ^ + 3 j ^ + &#946; k ^ and c &#8594; = - i ^…

Solution

Let a → = i ^ + 5 j ^ + α k ^ , b → = i ^ + 3 j ^ + β k ^ and c → = - i ^…