find lambda when the scaler projection of vector of A=lambda I+j+4k on b=2i+6j+3k is 4unit
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2
Answer:
Let
a
=λ
i
^
+
j
^
+4
k
^
and
b
=2
i
^
+6
j
^
+3
k
^
Given that projection of
a
on
b
is 4.
Projection of
a
on
b
is given by 4=
∣
b
∣
a
⋅
b
.
4=
2
2
+6
2
+3
2
(λ
i
^
+
j
^
+4
k
^
)⋅(2
i
^
+6
j
^
+3
k
^
)
⇒4=
49
2λ+6+12
⇒4=
7
2λ+18
⇒28=2λ+18
⇒2λ=28−18
⇒2λ=10
∴λ=5
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