Let a-3k- - b-2-3-4k- If projection of a- on b- is k-29- then the value of k-2 is

The correct option is A 9 GIVEN #160; a⃗=î+ĵ+3k̂ b⃗=2î 3ĵ+4k̂ Proj_ab=a⃗·b⃗ | b⃗ | Proj_ab=(î+ĵ+3k̂)·(2î 3ĵ+4k̂) | √(2^2+( 3)^2+4^2) ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

Let a⃗=î+ĵ+...

Question

Let $\to a =^i +^j + 3^k & \to b = 2^i - 3^j + 4^k$ . If projection of $\to a$ on $\to b$ is $\frac{k}{\sqrt{29}}$ , then the value of $(k - 2)$ is

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Solution

The correct option is A $9$
GIVEN
$\to a =^i +^j + 3^k$
$\to b = 2^i - 3^j + 4^k$
$P r o j_{a} b = \frac{\to a \cdot \to b}{∣ ∣ \to b ∣ ∣}$
$P r o j_{a} b = \frac{(^i +^j + 3^k) \cdot (2^i - 3^j + 4^k)}{∣ ∣ ∣ \sqrt{2^{2} + (- 3)^{2} + 4^{2}} ∣ ∣ ∣}$
$P r o j_{a} b = \frac{2 - 3 + 12}{\sqrt{4 + 9 + 16}}$
$P r o j_{a} b = \frac{11}{\sqrt{29}}$
comparing RHS with $\frac{k}{\sqrt{29}}$
$k = 11$
$k - 2 = 11 - 2$
$k - 2 = 9$

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Similar questions

Q. If

\to a

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\to b

are vectors such that

| \to a + \to b | = \sqrt{29}

and

\to a \times (2^i + 3^j + 4^k) = (2^i + 3^j + 4^k) \times \to b

, then a possible value of

(\to a + \to b) \cdot (- 7^i + 2^j + 3^k)

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\to a = 2^i -^j +^k, \to b =^i + 2^j -^k, \to c =^i +^j - 2^k

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and

\to c = r^i +^j + (2 r - 1)^k

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Let →a=^i+^j+3^k&→b=2^i−3^j+4^k. If projection of →a on →b is k√29, then the value of (k−2) is

The correct option is A 9GIVEN →a=^i+^j+3^k→b=2^i−3^j+4^kProjab=→a⋅→b∣∣→b∣∣Projab=(^i+^j+3^k)⋅(2^i−3^j+4^k)∣∣∣√22+(−3)2+42∣∣∣Projab=2−3+12√4+9+16Projab=11√29comparing RHS withk√29k=11k−2=11−2k−2=9

Let $\to a =^i +^j + 3^k & \to b = 2^i - 3^j + 4^k$ . If projection of $\to a$ on $\to b$ is $\frac{k}{\sqrt{29}}$ , then the value of $(k - 2)$ is