If \overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c} are three vectors such that \overrightarrow{a} \cdot \overrightarrow{b}=\overrightarrow{a} \cdot \overrightarrow{c} and \overrightarrow{a} \times \overrightarrow{b}= \overrightarrow{a} \times \overrightarrow{c}, \overrightarrow{a} \neq 0, then show that \overrightarrow{b}=\overrightarrow{c}. OR If |{ {\a}}^{\to}|=3,|{ {\b}}^{\to}|=5,|{ {\c}}^{\to}|=4 and { {\a}}^{\to}+{ {\b}}^{\to}+{ {\c}}^{\to}=\overrightarrow{0}, then find the value of (\overrightarrow{a} \cdot \overrightarrow{b}+\overrightarrow{b} \cdot \overrightarrow{c}+\overrightarrow{c} \cdot \overrightarrow{a})

CBSE Class 12 Math 2022 (Term II) Outside Delhi Set 2 Solved ...

SECTION - B
Question Nos. 7 to 10 carry 3 marks each.

Question : 2 of 4

Marks: +1, -0

{a}↖{→}, {b}↖{→}, {c}↖{→}

are three vectors such that

{a}↖{→} ⋅ {b}↖{→}={a}↖{→} ⋅ {c}↖{→}

and

{a}↖{→} × {b}↖{→}=

{a}↖{→} × {c}↖{→}, {a}↖{→} ≠ 0

, then show that

{b}↖{→}={c}↖{→}

.
OR
If

|{ {\a}}↖{→}|=3,|{ {\b}}↖{→}|=5,|{ {\c}}↖{→}|=4

and

{ {\a}}↖{→}+{ {\b}}↖{→}+{ {\c}}↖{→}={0}↖{→}

, then find the value of

({a}↖{→} ⋅ {b}↖{→}+{b}↖{→} ⋅ {c}↖{→}+{c}↖{→} ⋅ {a}↖{→})

Solution:

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