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Mathematics
Problem
If
a
⃗
=
(
i
−
j
+
7
k
)
\vec{a} = (i - j + 7k)
a
=
(
i
−
j
+
7
k
)
and
b
⃗
=
(
5
i
−
j
+
λ
k
)
\vec{b} = (5i - j + \lambda k)
b
=
(
5
i
−
j
+
λk
)
then find the value of
λ
\lambda
λ
so that
(
a
⃗
+
b
⃗
)
(\vec{a} + \vec{b})
(
a
+
b
)
and
(
a
⃗
−
b
⃗
)
(\vec{a} - \vec{b})
(
a
−
b
)
are orthogonal vectors. [CBSE 2013]
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