Find the angle between two vectors $straight a with rightwards arrow on top space and space straight b with rightwards arrow on top$ such that $open vertical bar straight a with rightwards arrow on top close vertical bar space equals space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 3$ and $straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 1$ .

Solution

Here $open vertical bar straight a with rightwards arrow on top close vertical bar$ = $open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 3 comma space space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 1$
Let $straight theta$ be the angle between $straight a with rightwards arrow on top space and space straight b with rightwards arrow on top.$
Now,
$straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space ab space cos space straight theta space space space space space space space space space space space space space space space rightwards double arrow space space space space 1 space equals space left parenthesis 3 right parenthesis thin space left parenthesis 3 right parenthesis space cos space straight theta rightwards double arrow space space space cos space straight theta space equals space 1 over 9 space space space space space space space space space space space space space space space space rightwards double arrow space space straight theta space equals space cos to the power of negative 1 end exponent open parentheses 1 over 9 close parentheses$

Some More Questions From Vector Algebra Chapter

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Vector Algebra

Some More Questions From Vector Algebra Chapter

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Vector Algebra

Find the angle between two vectors such that and .

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.10–19 coulomb

Classify the following measures as scalars and vectors.20 m/s2

Classify the following measures as scalars and vectors.time period

Classify the following measures as scalars and vectors.distance

Classify the following measures as scalars and vectors.force

Classify the following measures as scalars and vectors.velocity

Classify the following measures as scalars and vectors.work done

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Classify the following measures as scalars and vectors.
10^–19 coulomb

Classify the following measures as scalars and vectors.
20 m/s²

Classify the following measures as scalars and vectors.
time period

Classify the following measures as scalars and vectors.
distance

Classify the following measures as scalars and vectors.
force

Classify the following measures as scalars and vectors.
velocity

Classify the following measures as scalars and vectors.
work done