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Vector Addition

If A⃗ = 3 î...

Question

If $\to A = 3^i - 2^j +^k, \to B =^i - 3^j + 5^k a n d \to C = 2^i +^j - 4^k$ form a right angled triangle then out of the following which one is satisfied?

A

\to A = \to B + \to C a n d A^{2} = B^{2} + C^{2}

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B

\to A = \to B + \to C a n d B^{2} = A^{2} + C^{2}

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C

\to B = \to A + \to C a n d B^{2} = A^{2} + C^{2}

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D

\to B = \to A + \to C a n d A^{2} = B^{2} + C^{2}

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Solution

The correct option is A $\to A = \to B + \to C a n d B^{2} = A^{2} + C^{2}$
$\to A = 3^i - 2^j +^k$ and $A^{2} = 9 + 4 + 1 = 14$
$\to B =^i - 3^j + 5^k$ and $B^{2} = 1 + 9 + 25 = 35$
$\to C = 2^i +^j - 4^k$ and $C^{2} = 4 + 1 + 16 = 21$

Here, we see that,

$\to A = \to B + \to C$

And $B^{2} = A^{2} + C^{2}$

Hence, answer is option-(B).

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Similar questions

Q. Show that the vectors

\to a = 3^i - 2^j +^k, \to b =^i - 3^j + 5^k a n d \to c = 2^i +^j - 4^k

form a right angled triangle.

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

\to B = 3^i + 2^j + 4^k

, then find the value of

(\to A + \to B) \times (\to A - \to B)

.

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

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

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

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

(\to a \times \to b) \times (\to c \times \to d) =

\to A

\to B

\to A + \to B = \to C

A^{2} + B^{2} = C^{2}

θ

between positive directions of

\to A

\to B

\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}

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