Question

If A = 7i+2j-3k is parallel to B= 14i+4j+ak find the value of a

Answer 1

Answer:

106/119

Explanation:

since AllB

tita = 0°

A•B = 98+8-3a

= 106-3a

lAl = √7×7+2×2+(-3×-3)

= √49+4+9

= √62

lBl = √14×14+4×4+a×a

= √196+16+a×a

= √212+a×a

= 2a√54

A•B = lAl lBl cos0°

106-3a = √62 ×2a√54× 1

106-3a = 2a√62×54

106-3a = 2a√3348

106-3a = 2a×58

106-3a = 116a

106 = (116+3)a

a = 106/119

Answer 2

SOLUTION

GIVEN

Two vectors

$\vec{A} = 7 \hat{ \imath} + 2 \hat{ \jmath} - 3 \hat{k}$

$\vec{B} = 14\hat{ \imath} + 4 \hat{ \jmath} + a \hat{k}$

are parallel

TO DETERMINE

The value of a

EVALUATION

We know two given vectors are said to be parallel if their cross product is a zero vector

Now

$\vec{A} \times \vec{B}$

$= \displaystyle\begin{vmatrix} \hat{ \imath} & \hat{ \jmath} & \hat{k}\\ 7 & 2 & - 3 \\ 14 & 4 & a \end{vmatrix}$

Since given two vectors are parallel

$\displaystyle\begin{vmatrix} \hat{ \imath} & \hat{ \jmath} & \hat{k}\\ 7 & 2 & - 3 \\ 14 & 4 & a \end{vmatrix} = \hat{0}$

$\implies (2a + 12) \hat{ \imath} - (7a + 42) \hat{ \jmath} + (28 - 28) \hat{k} = \hat{0}$

Comparing both sides

$2a + 12 = 0$

$\implies \: 2a = - 12$

$\implies \: a = - 6$

FINAL ANSWER

The required value of a = - 6

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