Test Index

KEAM 2011 Math Paper

© examsnet.com

Question : 20 of 120

Marks: +1, -0

If the vector

8\hat{i}+a\hat{j}

of magnitude 10 is in the direction of the vector

4\hat{i}-3\hat{j},

then the value of a is equal to

6
3
$-3$
5
$-6$

Solution:

since, the vector

8i+aj

in the direction of the vector

4i-3j

. That means both vectors are parallel to each other.

By condition of parallel vectors,

\;\frac{8}{4}=\;\frac{a}{-3}

\Rightarrow a=-6

Alternative Method

Given also,

\;\;\left| 8i+aj \right|=10

\Rightarrow \;\; \sqrt{64+a^{2}}=10

\Rightarrow \;\; 64+a^{2}=100

\Rightarrow \;\; a^{2}=36

\Rightarrow \;\; a=\pm 6

(here we take (-) ve sign)

\Rightarrow \;\; a=-6

© examsnet.com

Go to Question:

Prev Question

Next Question