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Question
Mathematics
Let veca=5 hati- hatj-3 hatk and vecb= hati+3 hatj+5 hatk be two vectors. Then which one of the following statements is TRUE ?
Q. Let
a
=
5
i
^
−
j
^
−
3
k
^
and
b
=
i
^
+
3
j
^
+
5
k
^
be two vectors. Then which one of the following statements is TRUE ?
161
124
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JEE Main 2023
Vector Algebra
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A
Projection of
a
on
b
is
35
17
and the direction of the projection vector is same as of
b
.
B
Projection of
a
on
b
is
35
17
and the direction of the projection vector is opposite to the direction of
b
C
Projection of
a
on
b
is
35
−
17
and the direction of the projection vector is same as of
b
.
D
Projection of
a
on
b
is
35
−
17
and the direction of the projection vector is opposite to the direction of
b
.
Solution:
a
=
5
i
^
−
j
^
−
3
k
^
b
=
i
^
−
3
j
^
+
5
k
^
a
⋅
b
^
=
35
5
−
3
−
15
=
−
35
−
13