If k a → = 0 → , then what can you say about k and a → ?

Given: k a → = 0 → Here, when vector a → is multiplied by a scalar k , it gives a resultant 0 → .There are two cases: Suppose, a → = 2 , k = 0 ⇒ k a → = 0 → a → = 0 → , k = 1 ⇒ k a → = 0 → Or, a → = 0 → , k = 0 ⇒ k a → = 0 So, either k = 0 or a → = 0 → or k and a → both are 0 . Answer

If | a → | = 5 , then calculate - 1 2 a → .

Given: a → = 5 . To find, - 1 2 a → . So, = - 1 2 a → = - 1 2 a → = 1 2 a → ∵ - x = x = 1 2 × 5 = 5 2 Hence, value of - 1 2 a → is 5 2 .

If | a → | = 5 , then calculate - 1 2 a → .

Given: a → = 5 . To find, - 1 2 a → Here, - 1 2 is the scalar quantity. So, = - 1 2 a → = - 1 2 × 5 = - 5 2 Hence, the value of - 1 2 a → is - 5 2 .

For what value of p , is ( i ^ + j ^ + k ^ ) p a unit vector.

Let a → = p ( i ^ + j ^ + k ^ ) = p i ^ + p j ^ + p k ^ . Given that vector a → is a unit vector, a → = 1 . A vector whose magnitude is unity is called as unit vector. We know that, magnitude of vector a → is given by, a → = p 2 + p 2 + p 2 So, p 2 + p 2 + p 2 = 1 3 p 2 = 1 3 × p = 1 p = 1 3 ⇒ p = ± 1 3 Hence, for a → to be a unit vector, the value of p should be ± 1 3 .