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Exams
Joint Entrance Examination
Mathematics
Vector Algebra
Question 135
Question 135 of 379
Easy
MCQ
If the components of
a
⃗
=
α
i
^
+
β
j
^
+
γ
k
^
\vec a=\alpha\hat i+\beta\hat j+\gamma\hat k
a
=
α
i
^
+
β
j
^
+
γ
k
^
along and perpendicular to
b
⃗
=
3
i
^
+
j
^
−
k
^
\vec b=3\hat i+\hat j-\hat k
b
=
3
i
^
+
j
^
−
k
^
are
16
11
(
3
i
^
+
j
^
−
k
^
)
\dfrac{16}{11}(3\hat i+\hat j-\hat k)
11
16
(
3
i
^
+
j
^
−
k
^
)
and
1
11
(
−
4
i
^
−
5
j
^
−
17
k
^
)
\dfrac1{11}(-4\hat i-5\hat j-17\hat k)
11
1
(
−
4
i
^
−
5
j
^
−
17
k
^
)
respectively, then
α
2
+
β
2
+
γ
2
\alpha^2+\beta^2+\gamma^2
α
2
+
β
2
+
γ
2
is equal to:
A
16
B
23
C
26
D
18
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Official solution
\[\vec a = \frac{16}{11}(3,1,-1)+\frac1{11}(-4,-5,-17) = \left(\frac{48-4}{11},\frac{16-5}{11},\frac{-16-17}{11}\right) = (4,1,-3)\] \[\alpha^2+\beta^2+\gamma^2 = 16+1+9 = 26\]
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