amanamanuel097
Answered

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

Sagot :

bhargavnitesh291

Explanation:

We know that,

Magnitude of a unit vector is 1.

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

is [tex] \sf \sqrt{a^2+b^2+c^2 } [/tex]

The given vector is,

[tex]\sf \vec{A}= 0.3 \hat{i} + 0.4 \hat{j} + B \hat{k}[/tex]

Magnitude of the given vector is,

[tex]\sf | \vec{A}|= \sqrt{(0.3)^2+(0.4)^2+B^2} =1[/tex]

[tex]\sf \sqrt{0.09+0.16+B^2}=1[/tex]

[tex]\sf 0.25+B^2=1[/tex]

[tex]\sf B^2=1-0.25=0.75[/tex]

[tex]\sf B = \sqrt{0.75} ≈ 0.87[/tex]

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