Let a → = x i ^ + y j ^ + z k ^ and x = 2 y . If a → = 5 2 and a → makes an angle of 135 ° with the z -axis then a → =

Question

Let a &#8594; = x i ^ + y j ^ + z k ^ and x = 2 y . If a &#8594; = 5 2 and a &#8594; makes an angle of 135 &#176; with the z -axis then a &#8594; =

Aicharya · Accepted Answer

Given a &#8594; = x i ^ + y j ^ + z k ^ a &#8594; = x 2 + y 2 + z 2 = 5 y 2 + z 2 &#160; &#8757; x = 2 y i.e. 5 y 2 + z 2 = 5 2 &#8658; 5 y 2 + z 2 = 50 a &#8594; &#183; k ^ = a &#8594; cos 135 &#176; &#8658; z = 5 2 &#215; - 1 2 = - 5 Now, 5 y 2 = 25 &#8658; y = &#177; 5 , &#160; x = &#177; 2 5 i.e. a &#8594; = &#177; 2 5 i ^ &#177; 5 j ^ - 5 k ^

Let a → = x i ^ + y j ^ + z k ^ and x = 2 y . If a → = 5 2 and a → makes an angle of 135…

Solution

Let a &#8594; = x i ^ + y j ^ + z k ^ and x = 2 y . If a &#8594; = 5 2 and a &#8594; makes an angle of 135…

Solution

Let a → = x i ^ + y j ^ + z k ^ and x = 2 y . If a → = 5 2 and a → makes an angle of 135…