The vector in the direction of the vector hati-2 hatj +2 hatk that has magnitude 9 is

Question

The vector in the direction of the vector hati-2 hatj +2 hatk that has magnitude 9 is (A)  hati-2 hatj +2 hatk (B) ( hati-2 hatj +2 hatk/3) (C)  3( hati-2 hatj +2 hatk) (D)  9( hati-2 hatj +2 hatk)

Tardigrade Admin · Accepted Answer

Let a = hati-2 hatj +2 hatk | veca| = √ 1+ 4+ 4 = √9 = 3 ∴ Required vector =(9( hati-2 hatj +2 hatk)/3) = 3( hati-2 hatj +2 hatk)

Q. The vector in the direction of the vector $\hat{i} - 2 \hat{j} + 2 \hat{k}$ that has magnitude $9$ is

$\hat{i} - 2 \hat{j} + 2 \hat{k}$

$\frac{i ^ - 2 j ^ + 2 k ^}{3}$

$3 (\hat{i} - 2 \hat{j} + 2 \hat{k})$

$9 (\hat{i} - 2 \hat{j} + 2 \hat{k})$

Let $a = \hat{i} - 2 \hat{j} + 2 \hat{k}$
$∣ a ∣ = 1 + 4 + 4$
$= 9 = 3$
$∴$ Required vector $= \frac{9 ( i ^ - 2 j ^ + 2 k ^ )}{3}$
$= 3 (\hat{i} - 2 \hat{j} + 2 \hat{k})$

Q. The vector in the direction of the vector i^−2j^​+2k^ that has magnitude 9 is

i^−2j^​+2k^

3i^−2j^​+2k^​

3(i^−2j^​+2k^)

9(i^−2j^​+2k^)