Question

The given vector A=0.3i+0.4j+Bk is a unit vector the value of B is?​

Answer 1

Step-by-step explanation:

We know that,

Magnitude of a unit vector is 1.

and, magnitude of a vector in the form
`\sf a \hat{i}+b \hat{j} + c \hat{k}`

is
`\sf √(a^2+b^2+c^2 )`

The given vector is,

`\sf \vec{A}= 0.3 \hat{i} + 0.4 \hat{j} + B \hat{k}`

Magnitude of the given vector is,

`\sf | \vec{A}|= √((0.3)^2+(0.4)^2+B^2) =1`

`\sf √(0.09+0.16+B^2)=1`

`\sf 0.25+B^2=1`

`\sf B^2=1-0.25=0.75`

`\sf B = √(0.75) ≈ 0.87`