Let A B C D be a parallelogram such that \overrightarrow{A B}=\overrightarrow{q}, \overrightarrow{A D}=\overrightarrow{p} and \angle B A D be an acute angle. If \overrightarrow{r} is the vector that coincide with the altitude directed from the vertex B to the side A D, then \overrightarrow{r} is given by : [AIEEE 2012]

Correct Answer is : →r=−→q+(→p.q)(→p.p)→p

\overrightarrow{r}=3 \overrightarrow{q}- \overrightarrow{3({p \cdot q})}/\overrightarrow{({p \cdot p})} \overrightarrow{p}

\overrightarrow{r}=-\overrightarrow{q}+ \overrightarrow{({p . q})}/\overrightarrow{({p . p})} \overrightarrow{p}

\overrightarrow{r}=\overrightarrow{q}- \overrightarrow{({p} \cdot \overrightarrow{q})}/\overrightarrow{({p} \cdot \overrightarrow{p})} \overrightarrow{p}

\overrightarrow{r}=-3 \overrightarrow{q}- \overrightarrow{3({p \cdot q})}/\overrightarrow{({p \cdot p})}

AIEEE 2012 Solved Paper

Section: Mathematics

Question : 84 of 89

Marks: +1, -0

Let ABCD be a parallelogram such that

→

and ∠BAD be an acute angle. If

→

is the vector that coincide with the altitude directed from the vertex B to the side AD, then

→

is given by :

[AIEEE 2012]

→
r
=3
→
q
−‌
3(
→
p⋅q
)
(
→
p⋅p
)
→
p
→
r
=−
→
q
+‌
(
→
p.q
)
(
→
p.p
)
→
p
→
r
=
→
q
−‌
(
→
p
⋅
→
q
)
(
→
p
⋅
→
p
)
→
p
→
r
=−3
→
q
−‌
3(
→
p⋅q
)
(
→
p⋅p
)

Validate

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