The vector in the direction of the vector -2 -2 k- that has magnitude 9 isa -2 -2 k-b -2 -2 k-3c 3-2 -2 k-d 9-2 -2 k-

Let a⃗= î 2ĵ+2k̂ Any vector in the direction of a vector a⃗ is given by a⃗/|a⃗|. =î 2ĵ+2k̂/√(1^2+2^2+2^2)=î 2ĵ+2k̂/3 ∴ Vector in the direction of a⃗ with magnit ...

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Standard XII

Mathematics

Angle between Two Vectors

The vector in...

Question

The vector in the direction of the vector $^i - 2^j + 2^k$ that has magnitude 9 is

(a) $^i - 2^j + 2^k$

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

(c) $3 (^i - 2^j + 2^k)$

(d) $9 (^i - 2^j + 2^k)$

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Solution

Let $\to a =^i - 2^j + 2^k$

Any vector in the direction of a vector $\to a$ is given by $\frac{\to a}{| \to a |}$ .

$= \frac{^i - 2^j + 2^k}{\sqrt{1^{2} + 2^{2} + 2^{2}}} = \frac{^i - 2^j + 2^k}{3}$

$∴$ Vector in the direction of $\to a$ with magnitude 9 = $9. \frac{^i - 2^j + 2^k}{3}$

$= 3 (^i - 2^j + 2^k)$

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The vector in the direction of the vector ^i−2^j+2^k that has magnitude 9 is (a) ^i−2^j+2^k (b) ^i−2^j+2^k3 (c) 3(^i−2^j+2^k) (d) 9(^i−2^j+2^k)

Let →a=^i−2^j+2^k Any vector in the direction of a vector →a is given by →a|→a|. =^i−2^j+2^k√12+22+22=^i−2^j+2^k3 ∴ Vector in the direction of →a with magnitude 9 = 9.^i−2^j+2^k3 =3(^i−2^j+2^k)

The vector in the direction of the vector $^i - 2^j + 2^k$ that has magnitude 9 is

(a) $^i - 2^j + 2^k$

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

(c) $3 (^i - 2^j + 2^k)$

(d) $9 (^i - 2^j + 2^k)$