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Definition of Vector

If a⃗=xî+2ĵ...

Question

If $\to a = x^i + 2^j - z^k a n d \to b = 3^i - y j +^k$ are two equal vectors, then write the value
of $x + y + z$

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Solution

$\to a = x^i + 2^j - z^k$
$\to b = 3^i - y^j +^k$
both vectors are equal
$x^i + 2^j - z^k = 3^i - y^j +^k$
$x = 3, y = - 2, z = - 1$
$x + y + z = 3 - 2 - 1 = 0$

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Similar questions

\to a = x^i + 2^j - z^k

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

are two equal vectors, then write the value of

x + y + z

.

Q. If the vectors

\to a =^i +^j +^k, \to b =^i -^j + 2^k, \to c = x^i + (x - 2)^j -^k

are coplanar, then

x =

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

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

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

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

x \to a + y \to b + z \to c

x + y + z

\to a =^i +^j, \to b =^j +^k, \to c = α \to a + β \to b

and the vectors

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

are coplanar, then

\frac{α}{β} =

Q. Angle between the vectors

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

\to b = x^i +^j + (x + 1)^k

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