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Multiplication of a Vector by a Scalar

If a=i-j,b=...

Question

If $a = i - j, b = i + j, c = i + 3 j + 5 k$ and $n$ is a unit vector such that $b, n = 0, a, n = 0$ then the value of $| c, n |$ is equal to

A

1

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B

3

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C

5

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D

2

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Solution

The correct option is C $5$
$\begin{matrix} b_{n} = 0 (^i +^j) (a^i +^i e) = 0 a + b = c (-^j) (a^i + b^j) = 0 a - b = 0 a = 0 = b (¯ c \cdot ¯ n) (^i + 3^j + 5^b) \cdot (c^k) = 5 c = \sqrt{a^{2} + b^{2} + c^{2}} = 1 = 5 \end{matrix}$

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Similar questions

a > b > 0

I (n) = a^{1 / n} - b^{1 / n},

J (n) = (a - b)^{1 / n}

n \geq 2

\to u = ˆ i + ˆ j, \to v = ˆ i - ˆ j a n d \to w = ˆ i + 2 ˆ j + 3 ˆ k

ˆ n

is a unit vector such that

\to u . ˆ n = 0 a n d \to v . ˆ n = 0

∣ ∣ \to w . ˆ n ∣ ∣

(1 + x)^{n} = n \sum r = 0^{n} C_{r} x^{r}

n \sum r = 0 \frac{1}{^{n} C_{r}} = a,

then the value of

\sum 0 \leq i \leq n \sum 0 \leq j \leq n (\frac{i}{^{n} C_{i}} + \frac{j}{^{n} C_{j}})

\to u =^i +^j, \to v =^i -^j

\to w =^i + 2^j + 3^k

^n

is a unit vector such that

\to u .^n = 0

\to v .^n = 0

| \to w .^n | =

u = i + j, v = i - j

w = i + 2 j + 3 k

^n

is a unit vector such that

u \cdot^n = 0

v \cdot^n = 0

| w \cdot^n |

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