If r-3-2-5k- a-2-k- b-3-2k- and c-2-3k- such that r-la-mb-nc- then

If $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ where $\to a = 2^i + 3^j -^k, \to b = 3^i -^j +^k$ and $\to c =^i +^j + 3^k$ , then $\to r$ is equal to

Q. If

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

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

, and

\to a \times (\to b \times \to c) = p^i + q^j + r^k

, then

p + q + r =

Q. If

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

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

and

\to c = 3^i -^k

then, find the scalars

m

and

n

such that

\to c = m \to a + n \to b

Q. I: If

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

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

then

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

II: If

\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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If →r=3^i+2^j−5^k, →a=2^i−^j+^k, →b=^i+3^j−2^k and →c=−2^i+^j−3^k such that →r=l→a+m→b+n→c, then

The correct option is A l,n,m are in A.P3^i+2^j−5^k=L(2^i−^j+^k)+m(^i+3^j−2^k)+n(−2^i+^j−3^k)3=2l+m−2n2=−l+3m+n−5=l−2m−3n0=2l+2m−4n2n=m+lThus, l,n & m are in A.P.

If $\to r = 3^i + 2^j - 5^k, \to a = 2^i -^j +^k, \to b =^i + 3^j - 2^k$ and $\to c = - 2^i +^j - 3^k$ such that $\to r = l \to a + m \to b + n \to c$ , then

The correct option is A $l, n, m$ are in A. $P$
$3^i + 2^j - 5^k = L (2^i -^j +^k) + m (^i + 3^j - 2^k) + n (- 2^i +^j - 3^k)$

$3 = 2 l + m - 2 n$

$2 = - l + 3 m + n$

$- 5 = l - 2 m - 3 n$

$0 = 2 l + 2 m - 4 n$

$2 n = m + l$

Thus, $l, n$ & $m$ are in $A . P .$