If x-3-6-k- y-4-3k- and z-3-4-12k- then the magnitude of the projection of x-y- on z- is -

The correct option is C 14 Given: x⃗=3î 6ĵ k̂, y⃗=î+4ĵ 3k̂ Magnitude of projection of #160; ( x × y ) is #160; ( x × y #160;). z ...

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Byju's Answer

Standard XII

Mathematics

Properties of Iota

If x⃗=3î-6ĵ...

Question

If $\to x = 3^i - 6^j -^k, \to y =^i + 4^j - 3^k$ and $\to z = 3^i - 4^j - 12^k$ , then the magnitude of the projection of $\to x \times \to y$ on $\to z$ is :

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Solution

The correct option is C $14$
Given: $\to x = 3^i - 6^j -^k, \to y =^i + 4^j - 3^k$

Magnitude of projection of $(\to x \times \to y)$ is $\frac{(\to x \times \to y) . \to z}{∣ ∣ \to z ∣ ∣}$

$\to x \times \to y = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 3 & - 6 & - 1 1 & 4 & - 3 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 22^i + 8^j + 18^k$
.
$(\to x \times \to y) . \to z = 66 - 32 - 216 = - 182$

$∣ ∣ \to z ∣ ∣ = \sqrt{9 + 16 + 144} = 13$
Magnitude of projection of is $∣ ∣ ∣ \frac{- 182}{13} ∣ ∣ ∣ = 14$

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If →x=3^i−6^j−^k,→y=^i+4^j−3^k and →z=3^i−4^j−12^k, then the magnitude of the projection of →x×→y on →z is :

If $\to x = 3^i - 6^j -^k, \to y =^i + 4^j - 3^k$ and $\to z = 3^i - 4^j - 12^k$ , then the magnitude of the projection of $\to x \times \to y$ on $\to z$ is :