There are two vectors A-3- and B-2k- For these two vectorsi find the component of A- along B- and perpendicular to B- in vector form-ii If A- and B- are the adjacent sides of a parallelogram then find the magnitude of its area-iii find a unit vector which is perpendicular to both A- and B-

The correct option is A 1/5[ ĵ+2k̂ ], 3î+4/5ĵ 2/5k̂ ; 7 units ; 2/7î 6/7ĵ+3/7k̂ The component of A⃗ along B⃗ =A⃗.B⃗B⃗.B⃗B⃗ ...

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Multiplication with Vectors

There are two...

Question

There are two vectors $\to A = 3^i +^j$ and $\to B =^j + 2^k$ . For these two vectors
(i) find the component of $\to A$ along $\to B$ and perpendicular to $\to B$ in vector form.
(ii) If $\to A$ and $\to B$ are the adjacent sides of a parallelogram then find the magnitude of its area.
(iii) find a unit vector which is perpendicular to both $\to A$ and $\to B$ .

\frac{1}{5} (\begin{matrix} ^j + 2^k \end{matrix}), 3^i + \frac{4}{5}^j - \frac{2}{5}^k

;

7 u n i t s

;

\frac{2}{7}^i - \frac{6}{7}^j + \frac{3}{7}^k

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\frac{1}{4} (\begin{matrix} ^j + 2^k \end{matrix}), 3^i + \frac{4}{5}^j - \frac{2}{5}^k

;

9 u n i t s

;

\frac{2}{7}^i - \frac{6}{7}^j + \frac{3}{7}^k

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\frac{1}{5} (\begin{matrix} ^j + 2^k \end{matrix}),^i + \frac{4}{5}^j - \frac{2}{5}^k

;

9 u n i t s

;

\frac{2}{7}^i - \frac{6}{7}^j + \frac{3}{7}^k

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\frac{1}{4} (\begin{matrix} ^j + 2^k \end{matrix}), 3^i + \frac{4}{5}^j - \frac{2}{5}^k

;

7 u n i t s

;

\frac{3}{7}^i - \frac{5}{7}^j + \frac{3}{7}^k

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Solution

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| \to a \times \to b |

\to a =^i - 7^j + 7^k

\to b = 3^i - 2^j + 2^k

\to r = \to a + λ \to l

\to r = \to b + μ \to m

\to a = 5^i +^j + 2^k,

\to b = -^i + 7^j + 8^k,

\to l = - 4^i + 7^j -^k

\to m = - 2^i - 5^j - 7^k

a = 7^i - 4^j - 4^k a n d b = - 2^i -^j + 2^k

| c | = 5 \sqrt{6}

\to C

\to a = 7^i - 4^j - 4^k

\to b = - 2^i -^j + 2^k

| \to c | = 5 \sqrt{6}

$I f \to a = 2^i +^j + 3^k a n d \to b = 3^i + 5^j - 2^k, t h e n f i n d ∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣ .$

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