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Addition and Subtraction in Unit Vector Notation

A⃗=2î+ĵ,3ĵ-k̂...

Question

$\to A = 2^i +^j, 3^j -^k$ and $\to C = 6^i - 2^k$ . Value of $\to A - 2 \to B + 3 \to C$ would be

A

$20^i - 5^j + 4^k$

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B

$20^i - 5^j - 4^k$

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C

$4^i + 5^j + 20^k$

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D

$5^i + 4^j + 10^k$

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Solution

The correct option is B
$20^i - 5^j - 4^k$

$\to A - 2 \to B + 3 \to C = 2 (^i +^j) - 2 (3^j -^k) + 3 (6^i - 2^k)$
$= 2^i +^j - 6^j + 2^k + 18^i - 6^k = 20^i - 5^j - 4^k$

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Similar questions

\to A = 2^i +^j, B = 3^i -^k

\to C = 6^i - 2^k

\to A - 2 \to B + 3 \to C

\to A = 2^i +^j

\to B = 3^j -^k

\to C = 6^i - 2^k

. Find the value of

\to A - 2 \to B + 3 \to C

\to a = 3^i - 2^j +^k,

\to b = 2^i - 4^j - 3^k, \to c = -^i + 2^j + 2^k

\to a + \to b + \to c = 4^i - 4^j

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

, then magnitude of

\to a + 2 \to b - 3 \to c

\sqrt{78}

Q. Find the projection of

(\to a + 2 \to b)

\to c

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

\to c = 2^i -^j + 4^k

\to a = 2^i - 3^j + 4^k, \to b =^i -^j + 2^k

\to c = 6^i - 3^j +^k

\to d

which is perpendicular to both

\to a

\to b

\to c . \to d = 2

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Addition and Subtraction in Unit Vector Notation

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