Rd Sharma XII Vol 2 2019 Solutions for Class 12 Science Math Chapter 7 Scalar Triple Product are provided here with simple step-by-step explanations. These solutions for Scalar Triple Product are extremely popular among Class 12 Science students for Math Scalar Triple Product Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma XII Vol 2 2019 Book of Class 12 Science Math Chapter 7 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rd Sharma XII Vol 2 2019 Solutions. All Rd Sharma XII Vol 2 2019 Solutions for class Class 12 Science Math are prepared by experts and are 100% accurate.

Question 1:

Evaluate the following:
(i)

(ii)

Find , when
(i)

(ii)

Question 3:

Find the volume of the parallelopiped whose coterminous edges are represented by the vectors:
(i)

(ii)

(iii)

(iv)

Question 4:

Show the each of the following triads of vectors are coplanar:
(i)

(ii)

(iii)

Question 5:

Find the value of λ so that the following vectors are coplanar:
(i)

(ii)

(iii)

(iv)

Question 6:

Show that the four points having position vectors are not coplanar.

Question 7:

Show that the points A (−1, 4, −3), B (3, 2, −5), C (−3, 8, −5) and D (−3, 2, 1) are coplanar.

Question 8:

Show that four points whose position vectors are are coplanar.

Answer:

DISCLAIMER: Given points are not coplanar.

Question 9:

Find the value of λ for which the four points with position vectors are coplanar.

Prove that:

Question 11:

are the position vectors of points A, B and C respectively, prove that: is a vector perpendicular to the plane of triangle ABC.

Question 12:

(i) If c1 = 1 and c2 = 2, find c3 which makes coplanar.

(ii) If c2 = −1 and c3 = 1, show that no value of c1 can make coplanar.

Question 13:

Find λ for which the points A (3, 2, 1), B (4, λ, 5), C (4, 2, −2) and D (6, 5, −1) are coplanar.

Question 14:

If four points A, B, C and with position vectors 4$\stackrel{^}{i}+$3$\stackrel{^}{j}+$3$\stackrel{^}{k}$, 5$\stackrel{^}{i}+$ $x\stackrel{^}{j}+$ 7$\stackrel{^}{k}$, 5$\stackrel{^}{i}+$3$\stackrel{^}{j}$ and  respectively are coplanar, then find the value of x.

Answer:

Let  and $\stackrel{\to }{\mathrm{OD}}=7\stackrel{^}{i}+6\stackrel{^}{j}+\stackrel{^}{k}$.

$\therefore \stackrel{\to }{\mathrm{AB}}=\left(5\stackrel{^}{i}+x\stackrel{^}{j}+7\stackrel{^}{k}\right)-\left(4\stackrel{^}{i}+3\stackrel{^}{j}+3\stackrel{^}{k}\right)=\stackrel{^}{i}+\left(x-3\right)\stackrel{^}{j}+4\stackrel{^}{k}$

$\stackrel{\to }{\mathrm{AC}}=\left(5\stackrel{^}{i}+3\stackrel{^}{j}\right)-\left(4\stackrel{^}{i}+3\stackrel{^}{j}+3\stackrel{^}{k}\right)=\stackrel{^}{i}-3\stackrel{^}{k}$

$\stackrel{\to }{\mathrm{AD}}=\left(7\stackrel{^}{i}+6\stackrel{^}{j}+\stackrel{^}{k}\right)-\left(4\stackrel{^}{i}+3\stackrel{^}{j}+3\stackrel{^}{k}\right)=3\stackrel{^}{i}+3\stackrel{^}{j}-2\stackrel{^}{k}$

Since the given four points are coplanar, so the vectors  and $\stackrel{\to }{\mathrm{AD}}$ are also coplanar.

$\therefore \left[\begin{array}{ccc}\stackrel{\to }{\mathrm{AB}}& \stackrel{\to }{\mathrm{AC}}& \stackrel{\to }{\mathrm{AD}}\end{array}\right]=0$

$⇒\left|\begin{array}{ccc}1& x-3& 4\\ 1& 0& -3\\ 3& 3& -2\end{array}\right|=0\phantom{\rule{0ex}{0ex}}⇒1\left(0+9\right)-\left(x-3\right)\left(-2+9\right)+4\left(3-0\right)=0\phantom{\rule{0ex}{0ex}}⇒9-7x+21+12=0\phantom{\rule{0ex}{0ex}}⇒7x=42\phantom{\rule{0ex}{0ex}}⇒x=6$
Thus, the value of x is 6.

Question 1:

Write the value of

Question 2:

Write the value of

Question 3:

Write the value of

Question 4:

Find the values of 'a' for which the vectors are coplanar.

Question 5:

Find the volume of the parallelopiped with its edges represented by the vectors

Question 6:

If are non-collinear vectors, then find the value of

Question 7:

If the vectors (sec2 A) are coplanar, then find the value of cosec2 A + cosec2 B + cosec2 C.

Question 8:

For any two vectors of magnitudes 3 and 4 respectively, write the value of

Question 9:

If then find the value of λ + μ.

Question 10:

If are non-coplanar vectors, then find the value of

Question 11:

Find $\stackrel{\to }{a}.\left(\stackrel{\to }{b}×\stackrel{\to }{c}\right)$, if and $\stackrel{\to }{c}=3\stackrel{^}{i}+\stackrel{^}{j}+2\stackrel{^}{k}$.                    [CBSE 2014]

Answer:

The given vectors are and $\stackrel{\to }{c}=3\stackrel{^}{i}+\stackrel{^}{j}+2\stackrel{^}{k}$.

Now,

$\stackrel{\to }{b}×\stackrel{\to }{c}=\left|\begin{array}{ccc}\stackrel{^}{i}& \stackrel{^}{j}& \stackrel{^}{k}\\ -1& 2& 1\\ 3& 1& 2\end{array}\right|=3\stackrel{^}{i}+5\stackrel{^}{j}-7\stackrel{^}{k}$

$\therefore \stackrel{\to }{a}.\left(\stackrel{\to }{b}×\stackrel{\to }{c}\right)=\left(2\stackrel{^}{i}+\stackrel{^}{j}+3\stackrel{^}{k}\right).\left(3\stackrel{^}{i}+5\stackrel{^}{j}-7\stackrel{^}{k}\right)=2×3+1×5+3×\left(-7\right)=6+5-21=-10$

Question 1:

If lies in the plane of vectors , then which of the following is correct?
(a)

(b)

(c)

(d)

(a)

Question 2:

The value of
(a) 0
(b) 1
(c) 6
(d) none of these

(a) 0

Question 3:

If are three non-coplanar mutually perpendicular unit vectors, then is
(a) ± 1
(b) 0
(c) −2
(d) 2

Question 4:

If $\stackrel{\to }{r}·\stackrel{\to }{a}=\stackrel{\to }{r}·\stackrel{\to }{b}=\stackrel{\to }{r}·\stackrel{\to }{c}=0$ for some non-zero vector $\stackrel{\to }{r},$ then the value of is
(a) 2
(b) 3
(c) 0
(d) none of these

(c) 0

Question 5:

For any three vectors the expression equals
(a)

(b)

(c)

(d) none of these

Answer:

(d) none of these

Question 6:

If are non-coplanar vectors, then is equal to
(a) 0
(b) 2
(c) 1
(d) none of these

(a) 0

Question 7:

Let be three non-zero vectors such that is a unit vector perpendicular to both . If the angle between is $\frac{\mathrm{\pi }}{6},$ then ${\left|\begin{array}{ccc}{a}_{1}& {a}_{2}& {a}_{3}\\ {b}_{1}& {b}_{2}& {b}_{3}\\ {c}_{1}& {c}_{2}& {c}_{3}\end{array}\right|}^{2}$is equal to

(a) 0
(b) 1
(c)

(d)

(c)

Question 8:

If then the volume of the parallelopiped with conterminous edges is
(a) 2
(b) 1
(c) −1
(d) 0

Answer:

Disclaimer: None of the given options is correct.

If then λ + μ =
(a) 6
(b) −6
(c) 10
(d) 8

(a) 6

(a)

(b)

(c)

(d)

Question 11:

If the vectors are coplanar, then m =
(a) 0
(b) 38
(c) −10
(d) 10

Question 12:

For non-zero vectors the relation holds good, if
(a)

(b)

(c)

(d)

(a) 0

(b)

(c)

(d)

Question 14:

If are three non-coplanar vectors, then equals

(a) 0

(b)

(c)

(d)

is equal to

(a)

(b)

(c)

(d) 0

Answer:

View NCERT Solutions for all chapters of Class 12