Let a unit vector which makes an angle of 60^{\circ} with 2 \stackrel{\^}{ {\i}}+2 \stackrel{\^}{ {\j}}-\stackrel{\^}{ {\k}} and angle of 45^{\circ} with \stackrel{\^}{ {\i}}-\stackrel{\^}{ {\k}} be { {\C}}^{\to}. Then { {\C}}^{\to}+ (-\frac{1}{2} \stackrel{\^}{ {\i}}+ {1}/{3 \sqrt{2}} \stackrel{\^}{ {\j}}- {\sqrt{2}}/{3} \stackrel{\^}{ {\k}}) is : [4 Apr 2024 Shift 1]

Correct Answer is : √23^i−12^k

- {\sqrt{2}}/{3} \stackrel{\^}{ {\i}}+ {\sqrt{2}}/{3} \stackrel{\^}{ {\j}}+ (\frac{1}{2}+ {2 \sqrt{2}}/{3}) \stackrel{\^}{ {\k}}

{\sqrt{2}}/{3} \stackrel{\^}{i}+ {1}/{3 \sqrt{2}} \stackrel{\^}{j}-\frac{1}{2} \stackrel{\^}{k}

( {1}/{\sqrt{3}}+\frac{1}{2}) \stackrel{\^}{ {\i}}+ ( {1}/{\sqrt{3}}- {1}/{3 \sqrt{2}}) \stackrel{\^}{ {\j}}+ ( {1}/{\sqrt{3}}+ {\sqrt{2}}/{3}) \stackrel{\^}{ {\k}}

{\sqrt{2}}/{3} \stackrel{\^}{ {\i}}-\frac{1}{2} \stackrel{\^}{ {\k}}

Vector Algebra Part 3

Section: Mathematics

Question : 60 of 72

Marks: +1, -0

Let a unit vector which makes an angle of 60∘ with 2

−

and angle of 45∘ with

−

→

. Then

→

+(−‌

+‌

3√2

−‌

√2

) is :

[4 Apr 2024 Shift 1]

−‌
√2
3
^
i
+‌
√2
3
^
j
+(‌
1
2
+‌
2√2
3
)
^
k
‌
√2
3
^
i
+‌
1
3√2
^
j
−‌
1
2
^
k
(‌
1
√3
+‌
1
2
)
^
i
+(‌
1
√3
−‌
1
3√2
)
^
j
+(‌
1
√3
+‌
√2
3
)
^
k
‌
√2
3
^
i
−‌
1
2
^
k

Validate

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