The center and the radius of the sphere ≤ft|2{r}+(3{i}-{j}+4{k})|=4 are:

Correct Answer is : center =(−32,12,−2)=≤ft(-3/2,1/2,-2)=(−23,21,−2) and radius =2=2=2.

center =≤ft(3/2,-1/2,2) and radius =2.

center =≤ft(-3/2,1/2,-2) and radius =2.

center =≤ft(3/2,-1/2,2) and radius =1.

center =≤ft(-3/2,-1/2,2) and radius =1.

Correct Answer is : center =(−32,12,−2)=≤ft(-3/2,1/2,-2)=(−23,21,−2) and radius =2=2=2.

Test Index

UPSC NDA Math Model Paper 1

Question : 83 of 120

Marks: +1, -0

\left|2\vec{r}+(3\hat{i}-\hat{j}+4\hat{k})\right|=4

are:

Solution:

The given equation of the sphere is

\left|2\vec{r}+(3\hat{i}-\hat{j}+4\hat{k})\right|=4

Which can be re-written as

\left|\vec{r}-\left(-\frac{3}{2}\hat{i}+\frac{1}{2}\hat{j}-2\hat{k}\right)\right|=2

(dividing the LHS and RHS by 2).

Comparing this with the general equation

\left|\vec{r}-\vec{c}\right|=a

, we can say that

\vec{c}=-\frac{3}{2}\hat{i}+\frac{1}{2}\hat{j}-2\hat{k}

and

a=2

It means that the center is

\left(-\frac{3}{2},\frac{1}{2},-2\right)

and the radius is 2 .

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